Describing Motion Around Us

Distance, displacement, speed, velocity and acceleration, the three equations of motion, and reading distance–time and velocity–time graphs.

Key ideas

Distance is the total path; displacement is the straight-line change in position, with a direction.
Speed has no direction; velocity has one. Average speed = total distance ÷ total time.
Acceleration is the rate of change of velocity; it is negative (retardation) when an object slows down.
The slope of a distance–time graph gives speed; the slope of a velocity–time graph gives acceleration.
The area under a velocity–time graph gives the displacement.
Uniform circular motion has constant speed but changing direction, so it is accelerated.

Remember

Acceleration	a = (v − u) ÷ t
Equations of motion	v = u + at; s = ut + ½at²; v² − u² = 2as
Circular motion	v = 2πr ÷ t
Units	km/h × 5/18 = m/s

Watch out

Using km/h in an equation with m and s: convert first.
Taking u as 0 when the object does not start from rest.
Giving a distance when a displacement is asked (one full round has displacement 0).

Worked example

An athlete completes one round of a circular track of radius 28 m in 30 s. What distance has the athlete covered, and what is the displacement, after 135 s? (π = 22/7)

Working: 135 s = 4 ½ rounds; distance = 4 ½ × 2πr; displacement = diameter = 56 m

Answer: distance 792 m; displacement 56 m