Describing motion and motion graphs

Physics · Forces. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Distance is how far an object moves; it is a scalar. Displacement is the straight-line distance from start to finish with its direction; it is a vector. Speed is a scalar, and velocity is speed in a given direction. An object moving in a circle at constant speed has a changing velocity, because its direction keeps changing.

Acceleration is the change in velocity each second. A negative value means the object is slowing down.

Graphs tell the story of a journey. On a distance–time graph the gradient is the speed. On a velocity–time graph the gradient is the acceleration and the area under the line is the distance travelled.

Rules to remember

distance = speed × time (s = vt).
acceleration = change in velocity ÷ time taken (a = Δv/t); unit m/s².
(final velocity)² − (initial velocity)² = 2 × acceleration × distance (v² − u² = 2as).
Curved distance–time graph: speed at one time = gradient of the tangent at that time.
Typical speeds: walking 1.5 m/s, running 3 m/s, cycling 6 m/s, sound in air 330 m/s.
Free fall near the Earth: acceleration is about 9.8 m/s².
Terminal velocity: the resistive force equals the weight, the resultant force is zero, and the speed is constant.

Common mistake

Students read the height of a velocity–time graph as the distance. The distance is the area under the line; the gradient gives the acceleration.

Worked example

A car slows uniformly from 30 m/s to 10 m/s in 8.0 s. Find its acceleration and the distance it travels in this time.

a = Δv ÷ t = (10 − 30) ÷ 8.0 = −2.5 m/s².
Distance = area under the velocity–time line = average velocity × time = ½ × (30 + 10) × 8.0 = 160 m.
Check with v² − u² = 2as: 100 − 900 = −800, and 2 × (−2.5) × 160 = −800.

Answer: Acceleration −2.5 m/s² (a deceleration of 2.5 m/s²); distance 160 m

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