Motion & Kinematics — Chapter quiz · Physics & Environmental Science, Grade 12

Describe motion with graphs, vectors, and bounded constant-acceleration models.

Problem 1

A cyclist rides 6 km east, then 6 km west, returning to her starting point. What is the magnitude of her displacement?
Answer and explanation

0 km

She ends where she began, so her displacement is 0 km (even though she traveled 12 km of distance).

Problem 2

Which of the following is a scalar quantity?
  1. acceleration
  2. distance
  3. velocity
  4. displacement
Answer and explanation

distance

Distance has magnitude only, making it a scalar. Velocity, displacement, and acceleration are all vectors.

Problem 3

A car's velocity increases from 5 m/s to 25 m/s in 5.0 s. Find its acceleration.
Answer and explanation

4 m/s²

a = (v − v₀) ÷ t = (25 − 5) ÷ 5 = 20 ÷ 5 = 4 m/s².

Problem 4

A ball is dropped from rest and falls freely for 3.0 s. How fast is it moving? (g = 9.8 m/s²)
Answer and explanation

29.4 m/s

v = v₀ + gt = 0 + 9.8 × 3.0 = 29.4 m/s.

Problem 5

At the highest point of a vertical toss, a ball's velocity is momentarily zero. Its acceleration at that point is…
  1. 4.9 m/s² downward
  2. zero
  3. 9.8 m/s² downward
  4. 9.8 m/s² upward
Answer and explanation

9.8 m/s² downward

Gravity acts throughout the flight, so the acceleration is 9.8 m/s² downward even when the velocity is instantaneously zero.

Problem 6

A car starts from rest and accelerates at 4.0 m/s² for 5.0 s. Find its final velocity.
Answer and explanation

20 m/s

v = v₀ + at = 0 + (4.0)(5.0) = 20 m/s.

Problem 7

For that same car (from rest, 4.0 m/s² for 5.0 s), how far does it travel?
Answer and explanation

50 m

Δx = v₀t + ½at² = 0 + ½(4.0)(5.0²) = ½(4.0)(25) = 50 m.

Problem 8

On a velocity-time graph, the slope of the line represents the object's…
  1. displacement
  2. velocity
  3. distance
  4. acceleration
Answer and explanation

acceleration

Slope on a velocity-time graph is the change in velocity over time — that is, the acceleration.

Problem 9

A train moving at 24 m/s brakes at a constant −3.0 m/s². How far does it travel before stopping?
Answer and explanation

96 m

Use v² = v₀² + 2aΔx with v = 0: 0 = 24² + 2(−3.0)Δx, so 576 = 6Δx and Δx = 96 m.

Problem 10

Ignoring air resistance, the horizontal velocity of a projectile during its flight…
  1. stays constant
  2. decreases
  3. becomes zero at the top
  4. increases
Answer and explanation

stays constant

No horizontal force acts on the projectile, so its horizontal velocity stays constant for the whole flight.

Problem 11

A ball is thrown horizontally at 18 m/s from a 19.6 m high cliff. How far from the base does it land? (g = 9.8 m/s²)
Answer and explanation

36 m

Time to fall: 19.6 = 4.9t², so t² = 4.0 and t = 2.0 s. Range = (18)(2.0) = 36 m.

Problem 12

Explain why the horizontal and vertical motions of a projectile can be analyzed separately.
Answer and explanation

The two motions are independent: gravity only acts vertically, so the vertical motion is free fall (accelerating at g), while the horizontal motion has no force on it and stays at constant velocity. They share only the time in the air, so you can solve each as its own one-dimensional problem and link them through t.

Problem 13

Explain the following claim and supply a valid example or counterexample: Distance traveled and displacement can differ even on a straight line.
Answer and explanation

Distance 8 m; displacement+2 m with east positive. Distance traveled and displacement can differ even on a straight line.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 14

Independent chapter check: A student walks 12 m north in 6 s, then 4 m south in 4 s. Find average speed and average velocity, taking north positive.
Answer and explanation

Distance=16 m and elapsed time=10 s, so average speed=1.6 m/s. Displacement=+8 m, so average velocity=+0.8 m/s. Do not average the segment speeds without time weighting.

Distance=16 m and elapsed time=10 s, so average speed=1.6 m/s.

Displacement=+8 m, so average velocity=+0.8 m/s.

Do not average the segment speeds without time weighting.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 15

Explain the following claim and supply a valid example or counterexample: Negative acceleration need not mean slowing; compare its direction with velocity.
Answer and explanation

a=(−8+2)/3=−2 m/s²; speed increases because velocity and acceleration point together. Negative acceleration need not mean slowing; compare its direction with velocity.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 16

Independent chapter check: A cart changes from +8 to −4 m/s in 6 s under constant acceleration. Find acceleration, reversal time and displacement.
Answer and explanation

a=(−4−8)/6=−2 m/s². v=0 at 4 s. Displacement=8×6+½(−2)×6²=12 m; positive net displacement does not mean it moved east for the entire interval.

a=(−4−8)/6=−2 m/s². v=0 at 4 s.

Displacement=8×6+½(−2)×6²=12 m; positive net displacement does not mean it moved east for the entire interval.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 17

Explain the following claim and supply a valid example or counterexample: Constant-acceleration formulas do not apply across arbitrary changing acceleration.
Answer and explanation

Area of triangle=.5×4×6=12 m; acceleration slope=1.5 m/s². Constant-acceleration formulas do not apply across arbitrary changing acceleration.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 18

Independent chapter check: A car starts at 5 m/s and accelerates constantly at 2 m/s² for 3 s. Find final speed and displacement, then verify displacement from the velocity–time area.
Answer and explanation

v=5+2×3=11 m/s. Δx=5×3+½×2×9=24 m. The velocity–time trapezoid has area (5+11)/2×3=24 m, an independent representation of the same model.

v=5+2×3=11 m/s. Δx=5×3+½×2×9=24 m.

The velocity–time trapezoid has area (5+11)/2×3=24 m, an independent representation of the same model.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 19

Explain the following claim and supply a valid example or counterexample: Horizontal motion does not cancel gravity; independence assumes negligible air resistance.
Answer and explanation

Δx=vxt=6 m. Vertical fall is½gt²≈19.6 m withg=9.8 m/s². Horizontal motion does not cancel gravity; independence assumes negligible air resistance.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 20

Independent chapter check: A ball is launched horizontally at 8.0 m/s from a 19.6 m ledge. Ignore drag and use g=9.8 m/s². Find flight time, horizontal range and landing velocity components.
Answer and explanation

0=19.6−4.9t² gives t=2.00 s. Range=8×2=16.0 m. Landing velocity=(8.0,−19.6) m/s in right/up-positive axes; speed≈21.2 m/s.

0=19.6−4.9t² gives t=2.00 s.

Range=8×2=16.0 m.

Landing velocity=(8.0,−19.6) m/s in right/up-positive axes; speed≈21.2 m/s.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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