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Graphs of Motion · Form 4

Graphs of Motion: Practice Questions

Original SPM-style practice questions for Graphs of Motion, each with full worked solutions, Paper 1 multiple-choice and Paper 2 structured.

Written by the spmmath.com.my editorial team.

Original practice questions for Graphs of Motion, in the style of Mathematics Paper 1 (Objective) and Mathematics Paper 2 (Subjective). Each answer is worked so you can check your method, not just the result.

Multiple-choice (Paper 1 style)

Question 1

On a distance-time graph, a horizontal (flat) line segment represents an object that is:

  1. A. moving at constant speed
  2. B. at rest (stationary)
  3. C. accelerating uniformly
  4. D. decelerating uniformly

Question 2

The gradient of a distance-time graph gives the object's:

  1. A. distance
  2. B. speed
  3. C. acceleration
  4. D. time

Question 3

The area under a speed-time graph represents the:

  1. A. acceleration
  2. B. average speed
  3. C. distance travelled
  4. D. gradient

Question 4

The gradient of a speed-time graph represents the:

  1. A. distance
  2. B. speed
  3. C. acceleration
  4. D. time

Question 5

A car starts from rest and reaches a speed of 20 m/s in 8 s on a speed-time graph. Its acceleration is:

  1. A. 2.5 m/s²
  2. B. 0.4 m/s²
  3. C. 160 m/s²
  4. D. 28 m/s²

Question 6

On a speed-time graph an object moves at a constant speed of 15 m/s for 12 s. The distance travelled is:

  1. A. 180 m
  2. B. 27 m
  3. C. 1.25 m
  4. D. 90 m

Question 7

A motorcycle decelerates uniformly from 30 m/s to rest in 6 s. The distance travelled during this stage is:

  1. A. 90 m
  2. B. 180 m
  3. C. 5 m
  4. D. 15 m

Question 8

On a distance-time graph, a straight line goes from the origin to the point (4, 100), where time is in seconds and distance in metres. The line is then horizontal for the next 3 s.

The total distance travelled after 7 s is:

  1. A. 100 m
  2. B. 175 m
  3. C. 700 m
  4. D. 25 m

Question 9

On a speed-time graph, a straight line with a negative gradient represents an object that is:

  1. A. speeding up
  2. B. moving at constant speed
  3. C. decelerating (retarding)
  4. D. at rest

Question 10

During a journey shown on a speed-time graph, a bus covers a total distance of 300 m in a total time of 20 s (including a short stop). Its average speed is:

  1. A. 15 m/s
  2. B. 20 m/s
  3. C. 6000 m/s
  4. D. 0.067 m/s

Structured (Paper 2 style)

Question 1 (6 marks)

A particle moves along a straight line. Its speed-time graph consists of three stages: it starts from rest and accelerates uniformly to 24 m/s in 6 s, then travels at a constant 24 m/s for 10 s, and finally decelerates uniformly to rest in 8 s.

(a) Find the acceleration during the first stage. (b) Find the total distance travelled.

(c) Find the average speed for the whole journey.

  1. (a) Acceleration = gradient of first stage = (24 − 0) ÷ 6 = 4 m/s².
  2. (b) Stage 1 is a triangle: area = ½ × 6 × 24 = 72 m.
  3. Stage 2 is a rectangle: area = 24 × 10 = 240 m.
  4. Stage 3 is a triangle: area = ½ × 8 × 24 = 96 m.
  5. Total distance = 72 + 240 + 96 = 408 m.
  6. (c) Total time = 6 + 10 + 8 = 24 s, so average speed = total distance ÷ total time = 408 ÷ 24 = 17 m/s.

Question 2 (6 marks)

The distance-time graph of a cyclist shows the following journey: from 0 to 15 minutes he rides from home to a park 5 km away at a uniform speed; from 15 to 30 minutes he stays at the park; from 30 to 60 minutes he rides straight back home. (a) Find his speed during the first stage, in km/h.

(b) Describe his motion between the 15th and 30th minute. (c) Find his speed on the return journey, in km/h.

(d) Find the average speed for the whole journey, in km/h.

  1. (a) First stage: 15 minutes = 15 ÷ 60 = 0.25 h; speed = distance ÷ time = 5 ÷ 0.25 = 20 km/h.
  2. (b) The distance stays 5 km (a horizontal line), so the cyclist is at rest (stationary) at the park.
  3. (c) Return stage: 30 minutes = 0.5 h; speed = 5 ÷ 0.5 = 10 km/h.
  4. (d) Total distance = 5 + 5 = 10 km and total time = 60 minutes = 1 h.
  5. Average speed = total distance ÷ total time = 10 ÷ 1 = 10 km/h.

Question 3 (7 marks)

A bus starts from rest. Its speed-time graph has three stages: it accelerates uniformly for 5 s to reach a speed of v m/s, then travels at a constant v m/s for 20 s, and finally decelerates uniformly to rest in a further 10 s.

The total distance travelled is 550 m. (a) Write an expression, in terms of v, for the total distance travelled.

(b) Hence find the value of v. (c) Find the acceleration during the first stage.

(d) Find the deceleration during the last stage.

  1. (a) Stage 1 (triangle) = ½ × 5 × v = 2.5v; stage 2 (rectangle) = 20 × v = 20v; stage 3 (triangle) = ½ × 10 × v = 5v.
  2. Total distance = 2.5v + 20v + 5v = 27.5v.
  3. (b) 27.5v = 550, so v = 550 ÷ 27.5 = 20 m/s.
  4. (c) Acceleration = gradient of stage 1 = v ÷ 5 = 20 ÷ 5 = 4 m/s².
  5. (d) Deceleration = gradient of stage 3 = v ÷ 10 = 20 ÷ 10 = 2 m/s².

Question 4 (6 marks)

A motorcycle travels along a straight road. On its speed-time graph it accelerates uniformly from rest to 18 m/s in 6 s, then maintains 18 m/s for 10 s, and finally decelerates uniformly and stops after a further T s.

The total distance travelled is 342 m. (a) Find the distance travelled during the first stage.

(b) Find the distance travelled during the second stage. (c) Find the value of T.

(d) Find the deceleration during the last stage.

  1. (a) Stage 1 (triangle) = ½ × 6 × 18 = 54 m.
  2. (b) Stage 2 (rectangle) = 18 × 10 = 180 m.
  3. (c) Stage 3 (triangle) = ½ × T × 18 = 9T; total distance: 54 + 180 + 9T = 342.
  4. 234 + 9T = 342, so 9T = 108 and T = 12 s.
  5. (d) Deceleration = gradient of stage 3 = 18 ÷ T = 18 ÷ 12 = 1.5 m/s².

Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)

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Frequently asked questions

What's the difference between the Paper 1 and Paper 2 questions in this graphs of motion set?

Paper 1 questions are multiple-choice, testing quick reading of speed or distance from a given graph. Paper 2 questions ask you to draw a distance-time or speed-time graph from a description, then calculate speed, distance, or acceleration from it with full working shown.

Why should I attempt each question myself before checking the worked solution?

Reading gradient as speed and area under a speed-time graph as distance takes practice matching the right calculation to the right part of a graph. Attempting the question first shows whether you can do this under exam conditions, not just follow a finished solution's logic.

What common mistakes do students make with graphs of motion?

Students often confuse gradient with area, misread the time axis scale, or forget that a horizontal segment on a speed-time graph means constant speed, not rest. This practice set is designed to expose those slips before the real exam.

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