Motion

O Level / IGCSE Physics · Motion, forces and energy. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Speed is how much distance is covered in each second. Velocity is speed in a stated direction. Acceleration is how much the velocity changes in each second. If an object slows down, its acceleration is negative; this is called deceleration.

Acceleration is uniform when the velocity changes by the same amount every second, as for an object falling freely near the Earth with no air resistance. It is non-uniform when the change is different from second to second.

Most questions use graphs. Always read the label on the vertical axis first, because the same shape of line means different things on a distance-time graph and on a speed-time graph.

Rules to remember

Common mistake

A horizontal line means "at rest" on a distance-time graph but "constant speed" on a speed-time graph. Check which graph you have before you answer.

Worked example

A car starts from rest and accelerates uniformly to 18 m/s in 6.0 s. It then travels at a constant 18 m/s for 10 s. What is its acceleration in the first part, and what total distance does it travel?

  1. acceleration = change in velocity ÷ time = (18 − 0) ÷ 6.0 = 3.0 m/s2
  2. Distance while accelerating = area of the triangle = ½ × 6.0 × 18 = 54 m
  3. Distance at constant speed = area of the rectangle = 18 × 10 = 180 m
  4. Total distance = 54 + 180 = 234 m

Answer: Acceleration 3.0 m/s2; total distance 234 m.

Practice questions

Try each one, then open the answer.

1. On a speed–time graph, a straight line falls from 24 m/s at time 2.0 s to 0 m/s at time 8.0 s. What is the acceleration during this part of the motion?

  1. A
    −12 m/s2
  2. B
    −4.0 m/s2
  3. C
    −3.0 m/s2
  4. D
    +4.0 m/s2
Show answer

Answer: B. acceleration = change in speed ÷ time taken = (0 − 24) ÷ (8.0 − 2.0) = −4.0 m/s2. Dividing by 8.0 s instead of the 6.0 s interval gives −3.0 m/s2. The minus sign shows a deceleration.

2. A sprinter runs 100 m in 12.5 s. What is her average speed in km/h?

  1. A
    2.2 km/h
  2. B
    8.0 km/h
  3. C
    28.8 km/h
  4. D
    480 km/h
Show answer

Answer: C. Speed = 100 ÷ 12.5 = 8.0 m/s. In one hour she would go 8.0 × 3600 = 28 800 m = 28.8 km, so 28.8 km/h (multiply m/s by 3.6). Dividing by 3.6 gives 2.2 km/h.

3. A train increases its velocity from 10 m/s to 30 m/s in 8.0 s. What is its acceleration?

  1. A
    2.5 m/s2
  2. B
    3.75 m/s2
  3. C
    5.0 m/s2
  4. D
    160 m/s2
Show answer

Answer: A. acceleration = change in velocity ÷ time = (30 − 10) ÷ 8.0 = 2.5 m/s2.

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