Motion — Print · Physical Science: Matter, Forces & Energy, Grade 8

Speed, Velocity & Acceleration

Learning goals

• I can calculate average speed using speed = distance ÷ time.
• I can distinguish speed, velocity, and acceleration, and calculate acceleration from a change in velocity over time.

Readings for this unit

• A soft bumper stops a toy differently

Speed answers the everyday question, 'how fast is something moving?' You calculate it by dividing the distance traveled by the time it took: speed = distance ÷ time. If a cyclist rides 24 km in 3 hours, her average speed is 24 ÷ 3 = 8 km/h. That word 'average' matters, because she probably sped up on the flats and slowed on the hills — average speed smooths all of that into a single number for the whole trip.

Velocity takes speed and adds one crucial extra piece of information: direction. '8 km/h' is a speed, but '8 km/h heading north' is a velocity. This might sound like a fussy distinction, but it's a big deal in the real world. Two cars can share the exact same speed yet have completely different velocities if they're pointed different ways — and that difference is everything when they're both approaching the same intersection. Anytime an object turns, its velocity is changing even if its speed stays constant.

Acceleration measures how quickly velocity is changing — how fast you're speeding up, slowing down, or turning. Its formula is acceleration = (final velocity − initial velocity) ÷ time. Because it describes a change in velocity spread over a stretch of time, acceleration carries units like m/s² (meters per second, per second). A car that goes from 10 m/s to 25 m/s in 5 seconds is accelerating at (25 − 10) ÷ 5 = 3 m/s².

Acceleration can be positive or negative once a direction has been chosen positive. Its sign gives direction, not whether speed increases. With right positive, a right-moving cart with negative acceleration initially slows, while a left-moving cart with negative acceleration speeds up. Compare velocity and acceleration directions. Changing direction around a curve also changes velocity even if speed stays constant.

Keeping these three ideas straight is the backbone of describing any kind of motion. Speed tells you the pace, velocity pins down the pace and the heading, and acceleration captures how that motion is changing from moment to moment. Engineers use exactly these quantities to time traffic lights, design safe highway on-ramps, and figure out how much room a car needs to stop — the same math a radar gun uses to clock a driver going over the limit.

Average speed uses total distance divided by elapsed time. Average velocity uses displacement divided by elapsed time and includes direction. A round trip can have a nonzero average speed but zero average velocity because the final position equals the starting position.

Acceleration is change in velocity divided by elapsed time. Direction matters: a cart moving right and slowing has acceleration left. The sign of acceleration alone does not tell you whether speed increases; compare it with the velocity direction.

Keep units consistent before calculating. If position is in meters and time in seconds, speed is in m/s and acceleration in m/s². State an average when data cover an interval, since an average can hide different motions within it.

Speed

speed = distance ÷ time

distance in meters or km; time in seconds, minutes, or hours; speed in matching units like m/s or km/h.

Acceleration

a = (v final − v initial) ÷ t

v final and v initial are velocities in m/s; t is time in seconds; a comes out in m/s².

Worked examples

Avoid these mistakes

• A negative acceleration does not always mean an object is slowing down.

Words to know

speed

How fast an object moves, found by dividing distance traveled by the time it took.

velocity

Speed in a specific direction, like 60 km/h north.

acceleration

How quickly velocity changes over time, found by dividing the change in velocity by the time it took.

model

A representation that explains selected features and makes predictions; it leaves other details out.

evidence

Relevant observations or records used to support or challenge a claim.

system boundary

The chosen limit separating the objects being studied from their surroundings.

assumption

A condition taken as true for a model or calculation and needing to be checked against the case.

Average speed vs. the number on your speedometer

The speed = distance ÷ time formula gives you average speed over a whole trip, smoothing out every stoplight and highway stretch into one number. But your car's speedometer shows instantaneous speed — how fast you're going at that exact moment, which can be very different from the average. A trip with an average speed of 40 km/h might have included stretches at 0 km/h (stopped at lights) and 70 km/h (open highway); average speed just cannot capture that up-and-down detail, which is exactly why scientists use graphs to show motion changing moment to moment.

Reading motion straight off a graph

If you plot an object's distance against time, the slope (steepness) of that line is literally its speed — a steeper line means faster motion, and a flat line means the object has stopped. Plot velocity against time instead, and the slope becomes acceleration: a rising line means speeding up, a falling line means slowing down, and a flat line means constant velocity (zero acceleration). This is one of the most useful shortcuts in physics: instead of doing arithmetic, you can often just look at how steep — and which way — a graph tilts.

Galileo's ramps: clocking acceleration before stopwatches existed

In the early 1600s, Galileo Galilei wanted to study how falling objects accelerate, but free fall happens too fast to time accurately with the water clocks and pulse-counting available then. His clever workaround: roll a ball down a gently sloped ramp, which 'dilutes' gravity's pull and slows everything down enough to measure. By timing balls rolling different distances, Galileo showed that acceleration due to gravity is constant and doesn't depend on an object's weight — centuries before anyone had a precise clock, let alone a computer.

Acceleration is sneakier than 'speeding up' — turning counts too

Because velocity includes direction, any change in direction is technically acceleration — even if speed never changes at all. A car rounding a curve at a perfectly steady 50 km/h is still accelerating, because its direction is constantly changing; this is called centripetal acceleration. Pilots and astronauts describe strong accelerations in multiples of Earth's gravity, or 'g-forces' — a fighter jet pulling a tight turn might subject its pilot to 6–9 g's, meaning their body effectively feels 6 to 9 times heavier than normal, even though their speed might barely change.

In the real world

Traffic radar guns calculate a car's speed to catch drivers going faster than the posted limit.

Exit check

Over 20 s, what are average speed and velocity? Explain the relevant mechanism and one model limitation.

Reading Motion Graphs

Learning goals

• I can use a position–time graph to describe rest, direction, and relative speed.
• I can calculate average velocity over an interval from position and time data.

Readings for this unit

• A soft bumper stops a toy differently

A position–time graph shows where an object is relative to a chosen origin. Put time on the horizontal axis and position on the vertical axis. The slope tells average velocity over an interval: change in position divided by elapsed time. A graph shows a relationship, not necessarily the physical path the object traveled.

A horizontal segment means position stays the same: the object is at rest during that interval. A straight rising segment means constant positive velocity. A falling segment means motion in the negative direction, not automatically slowing down. Greater steepness means greater speed; the sign of the slope indicates direction.

Choose two data points within the interval you are studying. Subtract both the positions and times. On a curved position–time graph the velocity is changing. Do not confuse position–time with speed–time: a horizontal speed–time line means constant speed, which may be nonzero. Always read the axes first.

The slope of a position–time graph represents velocity. A horizontal segment means unchanged position, and a straight rising segment means constant positive velocity. A steep segment indicates a larger magnitude of velocity only when the axes and scales are comparable.

On a velocity–time graph, slope represents acceleration. A horizontal segment can mean moving at constant velocity, not standing still. The area between the graph and time axis represents displacement; a section below the axis contributes negative displacement.

Always identify which quantity is plotted before interpreting the shape. Use two points separated by a useful interval to calculate slope as vertical change divided by horizontal change. A line on a graph is not a picture of a hill or the actual path of the object.

Worked examples

Avoid these mistakes

• A downward line on a position graph does not mean the object moved downhill.

Words to know

position

Location relative to a chosen origin.

slope

Change in vertical value divided by change in horizontal value.

average velocity

Displacement divided by elapsed time, including direction.

model

A representation that explains selected features and makes predictions; it leaves other details out.

evidence

Relevant observations or records used to support or challenge a claim.

system boundary

The chosen limit separating the objects being studied from their surroundings.

assumption

A condition taken as true for a model or calculation and needing to be checked against the case.

In the real world

Exit check

Does the final downward line prove decreasing speed? Explain the relevant mechanism and one model limitation.

Newton's Three Laws of Motion

Learning goals

• I can state Newton's three laws of motion in my own words.
• I can apply Newton's second law (F = ma) to find force, mass, or acceleration.
• I can identify action-reaction force pairs.
• I can plan separate controlled force and mass comparisons.

Readings for this unit

• A soft bumper stops a toy differently

Isaac Newton tied together how forces and motion relate in just three elegant laws, and together they explain almost everything you see moving around you. Newton's first law is the law of inertia: an object at rest stays at rest, and an object already moving keeps moving at the same speed and in the same straight-line direction, unless an unbalanced force acts on it. Inertia is simply an object's built-in resistance to any change in its motion, and the more mass something has, the more inertia it has — that's why it's easy to stop a rolling tennis ball but nearly impossible to stop a rolling truck.

You feel the first law every time you ride in a car. When the car suddenly brakes, your body lurches forward — not because something pushed you, but because your body was already moving and 'wants' to keep moving until a force stops it. That force is your seatbelt, which is exactly why it can save your life. The same law explains why a stack of coins stays put when you flick the bottom one out, and why you slide sideways when a car turns sharply.

This first law also corrects one of the most common misunderstandings in all of physics: the belief that keeping something moving requires a constant push. It seems obvious from daily life — stop pedaling and your bike coasts to a halt. But the truth is the opposite: a moving object only slows down because hidden forces like friction and air resistance are pushing back on it. Remove those forces, as in the near-frictionless emptiness of deep space, and an object will glide onward forever with no engine at all.

Newton's second law puts numbers to all of this with one compact equation: F = ma, meaning force equals mass times acceleration. It says two intuitive things at once. First, the harder you push something, the more it accelerates. Second, the more mass an object has, the harder it resists that acceleration — which is why the same kick sends a soccer ball flying but barely budges a bowling ball. Force is measured in a unit called the newton (N), where 1 newton is the force needed to accelerate 1 kilogram at 1 m/s².

Newton's third law delivers the famous line: for every action force, there is an equal and opposite reaction force — and, crucially, those two forces act on different objects. When a swimmer's hands push water backward, the water pushes the swimmer forward with equal strength. When you jump, your legs push down on the Earth and the Earth pushes back up on you. The forces always come in matched pairs, pointing in opposite directions.

This third law is the secret behind how a rocket can fly through the vacuum of space, where there's nothing to push against. The rocket doesn't push on the air — it pushes a huge amount of hot gas downward out of its engines, and by Newton's third law that gas pushes the rocket upward with equal force. From walking (your feet push the ground backward so it pushes you forward) to a squid jetting through the ocean, these three laws together let you predict how any push or pull will change the way things move.

Newton's first law describes motion when net force is zero. The second law connects net force to acceleration: Fnet=ma. The third law identifies paired forces between two interacting objects. Use the law that addresses the question rather than memorizing isolated slogans.

A force diagram belongs to one object. If a hand pushes a cart, include the hand's force on the cart, not the cart's force on the hand. The latter belongs on the hand's diagram. Pair forces have equal magnitude, but different masses can have different accelerations.

For a fixed net force, a larger mass has a smaller acceleration. For a fixed mass, doubling net force doubles acceleration. These are model predictions that can be tested with repeated measurements; friction and measurement uncertainty can alter an ideal classroom result.

Build your understanding

Where this fits

This unit helps answer the chapter question: What evidence lets us describe and predict motion? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions.

Part 1 · Use inertia to explain persistence of motion

Newton’s first law describes constant velocity when the net external force is zero. Inertia is resistance to changes in velocity and increases with mass. A forward force is not required merely to maintain steady motion in the ideal case; everyday objects slow because resistance supplies an unbalanced force.

Read the visual model

Why is inertia not an extra force on a force diagram?

Visual reasoning — after your attempt

Inertia describes how mass resists acceleration. It is not an interaction from another object and should not be added as a force arrow.

A released toy cart slows due to interactions such as rolling resistance, not because motion uses up a stored force. A passenger’s motion changes when a seat or restraint exerts force; connect the law to interactions rather than calling inertia a pushing force.

Read the equal-time snapshots. The rest case overlaps at one position; the constant-velocity case moves the same distance each second. Neither needs a net forward force. Inertia describes resistance to a velocity change; it is not another force acting forward. Identify real interactions such as rolling resistance before explaining why an ordinary cart slows.

Pause and explain

Why is inertia not an extra force on a force diagram?

Check your reasoning after answering

Inertia describes how mass resists acceleration. It is not an interaction from another object and should not be added as a force arrow.

Part 2 · Use the net force in the second law

For the introductory constant-mass model, net force=mass×acceleration. Acceleration points in the net-force direction. A larger applied push does not automatically give larger acceleration if opposing forces or mass also change. Find the net force on one chosen object before using the equation.

Read the visual model

Which force belongs in F=ma for this calculation?

Visual reasoning — after your attempt

Use the net external force on the chosen cart, not a single applied force when other forces also act.

A 2 kg cart pushed right with 10 N against 4 N resistance has net force 6 N right and acceleration 3 m/s² right. Dividing 10 N by mass would ignore resistance and overestimate acceleration.

Read the red arrows on the cart, subtract opposite forces and then use the resulting net force. The green arrow is their summary and must not be counted as an additional interaction. A rightward acceleration could mean a right-moving cart speeds up or a left-moving cart slows; no present velocity was supplied by the force diagram.

Pause and explain

Which force belongs in F=ma for this calculation?

Check your reasoning after answering

Use the net external force on the chosen cart, not a single applied force when other forces also act.

Part 3 · Place third-law pairs on different objects

When object A exerts a force on B, B exerts an equal opposite force on A. These two forces act on different objects, so they do not cancel within one object’s force diagram. Balanced forces on a single object are a different kind of pair.

Read the visual model

Why do equal action-reaction forces not prevent the cart accelerating?

Visual reasoning — after your attempt

One force acts on the cart and the other on the hand. They are not both forces on the cart, so they cannot be canceled in its net-force calculation.

A hand pushes a cart and the cart pushes the hand equally in the opposite direction. The cart can accelerate because its own net force need not be zero. The two objects can have different accelerations because their masses and other interactions differ.

Pause and explain

Why do equal action-reaction forces not prevent the cart accelerating?

Check your reasoning after answering

One force acts on the cart and the other on the hand. They are not both forces on the cart, so they cannot be canceled in its net-force calculation.

Part 4 · Combine the laws in one explanation

A complete explanation names the object, its interacting partners, the net force, and the change in velocity. Use the first law when net force is zero, the second law for acceleration, and the third law to describe interaction partners. The laws answer related but different questions.

Read the visual model

Do equal interaction forces require equal accelerations?

Visual reasoning — after your attempt

No. Acceleration depends on each object’s mass and all forces acting on it. Equal opposite partner forces act on different objects.

For two carts with equal net force but different masses, the heavier cart has smaller acceleration. Each push still has an equal opposite partner force on the pusher. These facts are consistent because interaction-force equality is not acceleration equality.

The two graphs hold different quantities fixed. Left: mass is 2 kg, so a = Fnet/2 and acceleration increases in direct proportion to net force. Right: net force is 6 N, so a = 6/m and acceleration decreases with increasing mass along a curve. Do not change mass and force together and attribute the result to one factor. Repeated measurements can be compared with these model predictions without pretending the model curves are collected data.

Pause and explain

Do equal interaction forces require equal accelerations?

Check your reasoning after answering

No. Acceleration depends on each object’s mass and all forces acting on it. Equal opposite partner forces act on different objects.

Investigate force and mass separately

A change in a cart’s motion is not established by a force arrow alone. A planned comparison needs motion records, controls and a receiver.

Acceleration is the rate of velocity change, not the object’s current speed. To investigate its relation to net force, keep mass fixed and compare different controlled net forces. To investigate mass, keep net force fixed and compare masses. A horizontal force estimate must include opposing resistance; an applied pull during acceleration is not automatically the net force. An inertial reference is a frame where the introductory laws apply without additional apparent forces.

Define motion measurement before testing: specify the start, positive direction, time interval, and recorded positions or velocities. Equal-interval records can establish average velocities and their changes. Repeating a comparison reveals variation; it does not repair a method that changed both intended factors together. Use safe toy observations to investigate qualitative patterns only, or the supplied quantitative model data; do not invent a constant force from an unmeasured hand push.

Braking illustrates a net force opposite an existing motion direction. A right-moving cart under a leftward net force can slow before reversing. Friction, a brake pad or another interaction transfers energy into deformation and thermal changes. If force becomes balanced while the cart still moves, constant velocity can continue in the ideal model. The three laws connect persistence, net-force/mass response and separate interaction partners rather than provide three unrelated slogans.

Evidence to interpret

Mass (kg)	Net force (N)	Acceleration (m/s²)
1	1	1
1	2	2
2	2	1
4	2	0.5

Investigate or evaluate the supplied records

1. State one intended variable and choose matching record pairs.
2. Specify initial state, time measurements and a fixed positive direction.
3. Use supplied values or an approved safe simulation; ordinary hand-push observations do not provide calibrated net-force values.
4. Plot acceleration against the changed factor while identifying fixed conditions.
5. Plan repeated trials and a result that would challenge the explanation.

Explain and apply

Plan two comparisons from the records: one isolating net force, the other mass. Specify motion measurements, repeats, controls and what outcome would challenge the predicted relation. Explain braking separately from velocity direction.

• Design two separately controlled comparisons.
• Specify recorded motion, units and repeats.
• Explain a challenge result and braking mechanism.

Reasoning and marking guidance — after your attempt

Compare the 1 kg cases at 1 and 2 N to isolate net force; compare 1, 2 and 4 kg at 2 N to isolate mass. Match path, resisting conditions, timing, measuring procedure and initial state. Keep all repeated records. The supplied model gives a=Fnet/m; unexpected motion needs a boundary/force/method review rather than automatic rejection of conservation or hidden invented values. A leftward net force can slow rightward motion.

Apply the whole unit · Compare two carts

Illustrative trials: cart A has mass 2 kg and cart B mass 4 kg. Each receives a 10 N push right and 2 N resistance left. Both begin at rest; assume constant forces over the comparison interval.

Your task

Draw a force diagram for each cart, calculate acceleration, and describe how the first, second, and third laws apply. Label the partner force exerted on the pusher without adding it to the cart diagram.

What your response should show

• Use the supplied observations and measurements accurately; include units where needed.
• Explain the science behind your answer, rather than giving only a number or label.
• Show a labeled model, calculation, or evidence comparison as requested.
• State an assumption or limitation and suggest a useful next measurement.

Response guidance — after your attempt

Each cart has net force 8 N right. A accelerates at 4 m/s²; B at 2 m/s². Their velocities change because net force is nonzero. Each cart exerts a 10 N opposite force on its pusher, acting on the pusher rather than the cart. Equal applied forces and resistance do not imply equal acceleration when masses differ.

Scientific references and adapted teaching resources

• OpenSciEd 8.1 Contact Forces — public unit overview
• OpenSciEd instructional model — storyline routines
• Creative Commons Attribution 4.0 — middle-school material license

Parent / teacher teaching notes

Check each force with the sentence source acts on object. Require net-force subtraction before division by mass. Use a zero-net-force comparison to connect all three laws without suggesting they are separate unrelated rules. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation. The illustrated study “Investigate force and mass separately” is required curriculum content. Teach it before the associated application or distribute it over the assigned unit sessions; it is not an optional enrichment. Its practice/review/quiz response provides evidence of understanding. Model/data work must not be recorded as an actual physical experiment.

Newton's Second Law

F = ma

F is net force in newtons (N); m is mass in kg; a is acceleration in m/s². Rearranges to a = F ÷ m or m = F ÷ a.

Worked examples

Avoid these mistakes

• Third-law forces do not cancel on a single object.

Words to know

inertia

The tendency of an object to resist a change in its motion.

Newton's first law

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by an unbalanced force.

Newton's second law

Force equals mass times acceleration: F = ma.

Newton's third law

For every action force, there is an equal and opposite reaction force.

newton (N)

The unit used to measure force; 1 newton = 1 kg·m/s².

model

A representation that explains selected features and makes predictions; it leaves other details out.

evidence

Relevant observations or records used to support or challenge a claim.

system boundary

The chosen limit separating the objects being studied from their surroundings.

assumption

A condition taken as true for a model or calculation and needing to be checked against the case.

Newton stood on giants' shoulders — and corrected a 2,000-year-old mistake

The ancient Greek philosopher Aristotle taught that a constant force was needed to keep anything moving, and that objects naturally wanted to come to rest — an idea that felt intuitive and went essentially unquestioned for almost 2,000 years. Galileo's experiments with rolling balls suggested otherwise: on a perfectly frictionless surface, a moving object would just keep going forever. In 1687, Isaac Newton formalized this insight as his first law in a book called the Principia Mathematica, one of the most influential science books ever written, building directly on Galileo's and Johannes Kepler's earlier work.

Inertia depends on mass, not speed

It's tempting to think a fast-moving object has 'more inertia' than a slow one, but inertia only depends on mass — how much matter something has — not on how fast it's currently moving. A parked truck and a truck cruising at highway speed have exactly the same inertia (resistance to a change in motion), which is why it takes the same enormous force to start a heavy truck rolling as it does to bring it to a sudden stop. This is exactly why seatbelts and headrests exist: in a sudden stop, your body's inertia makes it want to keep moving forward (or your head want to stay still) even after the car has stopped.

Momentum and impulse: the hidden link between the second and third laws

Multiply an object's mass by its velocity and you get its momentum (p = mv) — a kind of 'quantity of motion.' It turns out force is really just how fast momentum changes: force × time = change in momentum. That's why airbags work: by stretching a car crash's stopping time from a fraction of a second into a slightly longer fraction of a second, the same change in momentum happens with much less force on your body. This connects directly to Newton's third law, too — the passenger pushes back on the airbag exactly as hard as the airbag pushes on the passenger.

Real rockets, real numbers: the third law at full throttle

The Saturn V rocket that carried astronauts to the Moon weighed nearly 3 million kilograms fully fueled, and its engines pushed exhaust gases downward with a combined thrust of over 34 million newtons at liftoff. By Newton's third law, that exhaust pushed back on the rocket with just as much force in the opposite direction — enough to overcome the rocket's enormous weight and accelerate it off the launch pad. No engine 'pushes against the air' the way a swimmer pushes against water; rockets work identically in the vacuum of space, since the action-reaction pair is between the rocket and its own exhaust, not the surrounding air.

In the real world

Newton's third law explains exactly how rockets launch into space — by pushing exhaust gas downward, they get pushed upward in return.

Exit check

What happens if mass and force both double? Explain the relevant mechanism and one model limitation.

Collisions, Deformation & Changes in Motion

Learning goals

• I can use before–during–after records to explain temporary and remaining deformation.
• I can compare matched collision records using force, mass, motion and energy with stated limits.

Readings for this unit

• A soft bumper stops a toy differently

A toy cart can hit soft packing material and stop without a permanent dent, while an otherwise similar collision against a hard stop can damage it. A collision is an interaction over a short interval when objects exert forces on each other.

Deformation means a change in shape. Elastic deformation is substantially reversed when the force is removed; permanent deformation remains.

Even a material that looks rigid can change shape slightly during contact. Study soft toy objects or supplied records, never a real phone, glass object, helmet or a person.

Temporary changes that escape normal-speed viewing can still matter to the explanation.

An observation is what a person or instrument records. An inference is a proposed interpretation of those records. Keep the two separate: a graph can show a pattern while more than one mechanism might explain it. State the chosen system, or part of the world being studied, and its boundary before accounting for material or energy transfers.

Use each figure as a reasoning tool. Read its caption and labels, describe the pattern, then explain a cause. If the picture is schematic, use the stated numbers rather than measuring its printed size. Check whether its simplified conditions match the problem before applying a formula.

Build your understanding

Where this fits

This unit helps answer the chapter question: What evidence lets us describe and predict motion? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions.

Part 1 · Compare before, during and after contact

Observations before contact establish motion and shape; observations during contact can reveal bending or compression; afterward they show rebound or permanent change. A system model includes both objects and their surroundings. A cartoon with three frames is a model, not proof of unseen changes.

Read the visual model

A timeline is important because different interactions exist at different stages. An elastic collision is an ideal case where the system’s kinetic energy is retained after separation. A damaged or thermally dissipative collision can have a different outcome.

Why should the contact-force arrows not be carried into the separated after-collision snapshot?

Visual reasoning — after your attempt

The contact interaction has ended once the carts separate. A remaining velocity is not evidence of a continuing contact push; other real interactions must be named separately.

Illustrative foam bumper images show 20 mm thickness before contact, 12 mm during contact and 19 mm afterward. The shape mostly recovers but not exactly. A slow record permits an observation that a single after-collision photograph would miss.

Pause and explain

Why is an afterward photograph insufficient to detect temporary deformation?

Check your reasoning after answering

An object can deform during contact and then recover. The after-image does not show the complete time sequence.

Part 2 · Connect equal forces with different motion changes

During contact, each object exerts an equal-size opposite-direction force on the other. Different masses can undergo different accelerations under these equal interaction forces. For each object, include other forces before calculating a net force.

Read the visual model

Force equality belongs to the interaction pair. Acceleration also depends on the receiver’s mass and full force account. Calculate a change in velocity separately from the object’s already existing velocity.

Over an interval of 0.1 s at these average forces, what are the velocity changes?

Visual reasoning — after your attempt

A changes by 0.5 m/s left and B by 1 m/s right. Their acceleration and velocity changes differ even though the paired interaction forces are equal.

If the contact force dominates, a 1 kg cart and a 2 kg cart under equal 4 N contact forces have acceleration magnitudes 4 and 2 m/s². Metres per second squared describes the rate of velocity change, not the distance travelled.

Pause and explain

Does greater acceleration of the lighter cart imply a larger collision force on it?

Check your reasoning after answering

No. Equal interaction forces can cause different acceleration because masses differ, and net-force calculations must account for other forces.

Part 3 · Track energy and deformation without a damage shortcut

Kinetic energy is energy associated with motion. In the same simplified situation, more mass at the same speed means more kinetic energy, and doubling speed gives four times the kinetic energy. During stopping, energy can transfer into temporary deformation, thermal changes, sound and surroundings.

Read the visual model

A system boundary determines which energy changes are included. Temporary deformation may later release stored energy; permanent change and warming can remain. Specify the stage of the collision before deciding what the bars represent.

How much kinetic energy is no longer in motion here, and why is calling it destroyed incorrect?

Visual reasoning — after your attempt

2 J is no longer kinetic in this account. It is represented by thermal and deformation changes inside the stated full system, so total energy remains 4 J.

A supplied cart model has 1 J at one speed and 4 J at twice that speed. The energy ratio is useful, but damage also depends on contact area, material, duration and breaking limits. Equal energy does not guarantee equal damage.

Pause and explain

Can speed alone predict every dent?

Check your reasoning after answering

No. It influences motion energy, but material response, geometry and how the object stops also affect damage.

Part 4 · Evaluate a cushioning mechanism

Cushioning can allow a moving object to stop through a longer distance and time, often reducing typical and peak stopping forces for comparable starting motion. A peak force is the largest recorded force; it differs from the average over contact. A cushion that bottoms out can lose that advantage.

Read the visual model

Start with the time width and force height. Average force can be found from the measured velocity change and stopping time in this model. The force–time area is an optional further connection; it does not have units of distance or energy.

Compare average forces using mass×velocity change/time. Why is “soft-looking always protects” too strong?

Visual reasoning — after your attempt

The averages are 0.2×2/0.02 = 20 N and 0.2×2/0.08 = 5 N. Longer stopping time can reduce force for the same motion change, but a material may bottom out, change the stopping conditions or fail another requirement.

Illustrative tests for matched carts at the same speed show peak readings of 18, 19, 20 N without padding and 9, 10, 11 N with padding. Check repeated trials, measuring method and pad thickness before generalizing to other objects.

Pause and explain

What do these peak records support?

Check your reasoning after answering

Lower measured peak force for this padded setup under the stated matched conditions. They do not certify every pad or establish identical average forces or injury protection.

Apply the whole unit · Temporary shape and a peak reading

Illustrative case for analysis, not measurements collected by the learner. Illustrative matched-cart tests show bumper thickness 15 mm before, 8 mm during and 15 mm afterward; peak force is 12 N rather than 24 N for a rigid stop.

Your task

Explain the temporary deformation and compare peak values without declaring all collisions safe. Use the supplied conditions, show intermediate reasoning and distinguish the supported conclusion from a broader claim.

What your response should show

• Use the specified quantities and units.
• Explain an intermediate step or comparison.
• Connect the pattern to the physical mechanism.
• State an assumption or limitation.

Response guidance — after your attempt

1. Compare thickness at three times: 15→8→15 mm shows compression and recovery in the record.

2. Classify the modeled shape change as elastic because its thickness recovers.

3. Compare peaks: 12/24=0.5, so the padded peak is half the rigid-stop peak under matched conditions.

4. Relate cushioning to stopping time/distance and account for redistributed energy, while limiting the claim to these records.

The bumper undergoes elastic deformation in this simplified record because it regains its thickness. The padded peak is half the rigid-stop peak under matched conditions. Deformation can allow a longer stopping interval, but the readings do not prove that every object is protected or give the entire force–time history. Energy is redistributed rather than erased.

Scientific references and adapted teaching resources

• OpenSciEd 8.1 Contact Forces — public unit overview
• OpenSciEd instructional model — storyline routines
• Creative Commons Attribution 4.0 — middle-school material license
• OpenSciEd 8.1 Lesson 2 — Exploring Horizontal Collisions (public handout)

Parent / teacher teaching notes

Ask the learner to describe the phenomenon before naming a formula. Discuss each checkpoint after an attempt. Use the supplied records when equipment is unavailable and label them illustrative rather than actual measurements. The final explanation should identify a mechanism and a limit, with different defensible wording accepted. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation.

Worked examples

Avoid these mistakes

• It may have changed temporarily during contact; use a before–during–after record.
• Do not treat a schematic drawing as a scale measurement or a universal guarantee.
• Keep the stated comparison conditions and measurement boundary explicit.
• A correct numerical result needs units and an explanation of its meaning.

Words to know

collision

Short interaction in which objects exert forces on each other.

deformation

Change in an object’s shape.

elastic deformation

Shape change that substantially reverses after the force is removed.

permanent deformation

Shape change remaining after the interaction.

peak force

Largest force recorded during a specified interval.

model

A representation that explains selected features and makes predictions; it leaves other details out.

evidence

Relevant observations or records used to support or challenge a claim.

system boundary

The chosen limit separating the objects being studied from their surroundings.

assumption

A condition taken as true for a model or calculation and needing to be checked against the case.

In the real world

Illustrative matched-cart tests show bumper thickness 15 mm before, 8 mm during and 15 mm afterward; peak force is 12 N rather than 24 N for a rigid stop.

Exit check

Does recovered thickness establish that no energy transferred? Explain the relevant mechanism and one model limitation.

Designing & Revising a Collision Protector

Learning goals

• I can define a protector’s criteria and constraints and evaluate repeated test records.
• I can propose a mechanism-based revision and plan a controlled retest.

Readings for this unit

• A soft bumper stops a toy differently

Engineering uses scientific evidence to solve a defined problem. A criterion is a feature used to judge success, such as keeping a model payload undamaged.

A constraint is a limit, such as maximum size or cost. A stakeholder is someone affected by a design.

A good protector must satisfy the actual task, not merely contain the most padding. Use a soft toy model and supplied records; do not use people, animals, real electronics, fragile glass or certification claims about safety equipment.

The design cycle is iterative: testing informs a revision, and the revised solution must be tested again.

An observation is what a person or instrument records. An inference is a proposed interpretation of those records. Keep the two separate: a graph can show a pattern while more than one mechanism might explain it. State the chosen system, or part of the world being studied, and its boundary before accounting for material or energy transfers.

Use each figure as a reasoning tool. Read its caption and labels, describe the pattern, then explain a cause. If the picture is schematic, use the stated numbers rather than measuring its printed size. Check whether its simplified conditions match the problem before applying a formula.

Build your understanding

Where this fits

This unit helps answer the chapter question: What evidence lets us describe and predict motion? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions.

Part 1 · Define success and the limits before testing

Specify the protected object, collision conditions, damage measure and permitted resources. Operational definition means exactly how a property will be judged in the test. A visible mark on a paper target can be a model damage indicator, but it is not a measurement of real injury.

Read the visual model

Why define the dent measure before seeing results?

Visual reasoning — after your attempt

A fixed rule allows consistent judgments and avoids changing success criteria to favor a preferred design.

A toy protector may need to leave no permanent target dent, fit within 5 cm thickness and use at most 20 g of padding. A design that exceeds a hard limit does not qualify even if its force reading is lower.

Pause and explain

Why define the dent measure before seeing results?

Check your reasoning after answering

A fixed rule allows consistent judgments and avoids changing success criteria to favor a preferred design.

Part 2 · Predict how a feature could work

An initial design model should connect a physical feature to a mechanism. Compressible padding can increase stopping distance; a broad face can distribute contact over greater area. These are different mechanisms and need different observations. More padding can add mass or run out of compression space.

Read the visual model

A mechanism explains how the feature changes the interaction. OpenSciEd’s ring sketches below give concrete shapes to compare, but an unloaded drawing cannot establish their performance. Predict, test, revise and retest.

Which measurement could distinguish “more travel” from “a prettier design”?

Visual reasoning — after your attempt

Measure deformation or stopping distance/time under matched loads and then evaluate peak-force/damage criteria using an appropriate safe test or supplied records.

Sketch two designs with the same total padding amount but different arrangements. Predict the shape changes during contact and identify the measurement that could distinguish the ideas. Drawing a thick case alone is not an explanation.

Pause and explain

Does a larger contact face automatically mean a smaller total force?

Check your reasoning after answering

No. It can lower pressure for the same force by spreading contact area, but total force depends on the stopping interaction.

Part 3 · Compare repeated tests under matched conditions

Hold starting speed, payload mass, collision direction, surface and measuring procedure comparable. Repeat with fresh or restored samples when previous deformation affects results. Keep all planned measurements, including inconvenient failures. A mean is the sum divided by the number of readings; a range is maximum minus minimum.

Read the visual model

State whether a requirement concerns a mean, a maximum or every trial. Different definitions lead to different decisions. Graphing both the mean and trials helps a parent or reviewer see the evidence instead of relying on one favorable result.

Which design meets the stated force limit in all three trials? Why must C’s 48 N reading remain in the report?

Visual reasoning — after your attempt

Only B does. C fails one trial even though two are below the limit; omitting the 48 N record would misrepresent reliability and the actual criterion.

Illustrative peaks for A are 12, 14, 13 N and for B 10, 11, 15 N. A averages 13 N with range 2 N; B averages 12 N with range 5 N. B has a lower mean but greater variability.

Pause and explain

Why is B’s single 10 N reading an incomplete comparison?

Check your reasoning after answering

It omits its other readings and variability. Evaluate all planned trials along with constraints and damage observations.

Part 4 · Revise and transfer the explanation

Choose a revision from evidence, then predict what should change and retest. A design can be strongest for one criterion and weaker for another. A transfer assessment asks whether the mechanism still applies in a new setting, rather than whether the student remembers a brand or drawing.

Read the visual model

Transfer means applying an explanation to a new situation. Keep the mechanism explicit: which part should deform, what motion change should occur, and which constraint might fail? A prediction is not an already completed retest.

Does passing three horizontal tests guarantee a successful corner impact? Name one changed condition to test.

Visual reasoning — after your attempt

No. Orientation/contact area or the stopping path changes. Define a safe comparable corner-impact test or analyze supplied records and evaluate the same stated criteria.

Combine A’s stable arrangement with B’s more compressible layer if the size and mass limits allow it. Predict reduced typical peak while retaining consistency, then collect new data. The combination is a proposal until tested.

Pause and explain

Does combining useful features prove the new protector is better?

Check your reasoning after answering

No. Features can interact and violate limits. The revised design requires new tests under the same evaluation rules.

Apply the whole unit · A design decision with a hard constraint

Illustrative case for analysis, not measurements collected by the learner. Illustrative designs have A: mean peak 13 N, thickness 4 cm; B: mean peak 9 N, thickness 7 cm. Maximum permitted thickness is 5 cm.

Your task

Choose a qualifying starting design and propose an evidence-based revision. Use the supplied conditions, show intermediate reasoning and distinguish the supported conclusion from a broader claim.

What your response should show

• Use the specified quantities and units.
• Explain an intermediate step or comparison.
• Connect the pattern to the physical mechanism.
• State an assumption or limitation.

Response guidance — after your attempt

1. Read the hard thickness limit before ranking peak force.

2. A at 4 cm satisfies the 5 cm limit; B at 7 cm does not.

3. Choose A as a qualifying starting design, not as proof of universally best protection.

4. Propose a changed padding arrangement within 5 cm and retest with matched motion, repeated peaks and deformation records.

A qualifies under the thickness rule; B does not despite its lower mean peak. Start with A and investigate whether a more compressible arrangement within 5 cm lowers the peak. Repeat matched tests, record all results and evaluate permanent deformation as well as force. Lower mean peak alone is not universal protection.

Scientific references and adapted teaching resources

• OpenSciEd 8.1 Contact Forces — public unit overview
• OpenSciEd instructional model — storyline routines
• Creative Commons Attribution 4.0 — middle-school material license
• OpenSciEd 8.1 Lesson 13 — Exploring shape of a cushioning material (public handout)

Parent / teacher teaching notes

Ask the learner to describe the phenomenon before naming a formula. Discuss each checkpoint after an attempt. Use the supplied records when equipment is unavailable and label them illustrative rather than actual measurements. The final explanation should identify a mechanism and a limit, with different defensible wording accepted. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation.

Worked examples

Avoid these mistakes

• Judge repeated evidence, variability, damage measures and hard constraints, rather than one selected reading.
• Do not treat a schematic drawing as a scale measurement or a universal guarantee.
• Keep the stated comparison conditions and measurement boundary explicit.
• A correct numerical result needs units and an explanation of its meaning.

Words to know

criterion

Feature used to evaluate success.

constraint

Limit a design must meet.

stakeholder

Person or group affected by the design.

operational definition

Stated rule for measuring or judging a property.

iteration

Another test-and-revision cycle informed by evidence.

model

A representation that explains selected features and makes predictions; it leaves other details out.

evidence

Relevant observations or records used to support or challenge a claim.

system boundary

The chosen limit separating the objects being studied from their surroundings.

assumption

A condition taken as true for a model or calculation and needing to be checked against the case.

In the real world

Illustrative designs have A: mean peak 13 N, thickness 4 cm; B: mean peak 9 N, thickness 7 cm. Maximum permitted thickness is 5 cm.

Exit check

Which is a qualifying starting design under the stated limit? Explain the relevant mechanism and one model limitation.