K323 / 2027
Kinematics overview

Topic 2 of 6

Acceleration and slowing down

Acceleration is the change in velocity per unit time.

Velocity includes direction. If that distinction is unfamiliar, review speed and velocity first.

Uniform acceleration means equal changes in velocity in equal time intervals. If velocity rises from 0 to 2 to 4 to 6 m/s at one-second intervals along a straight line, the acceleration is 2 m/s2. Every second adds another 2 m/s of velocity.

a = (v - u) / tu = initial velocity, v = final velocity, t = elapsed time. Acceleration a is measured in m/s2.

This gives the acceleration throughout an interval if it is uniform. If it varies, the calculation gives the average acceleration over that interval.

Worked example

Acceleration while slowing down

A trolley moving forwards slows uniformly from 8 m/s to 2 m/s in 3 s. Take forwards as positive.

a = (2 - 8) / 3 = -2 m/s2

The velocity decreases by 2 m/s each second. It still moves forwards throughout, because its velocity stays positive. We can also say it has a deceleration of 2 m/s2.

For non-uniform acceleration, the velocity changes by different amounts in equal times. A car leaving a junction may gain 2 m/s in its first second, then 3 m/s in the next, then only 1 m/s as the driver eases off. It speeds up in each interval, but not at a constant rate.

Negative acceleration does not always mean slowing. If velocity changes from -2 to -5 m/s, speed increases from 2 to 5 m/s. Velocity and acceleration point in the same negative direction. A body slows when acceleration opposes its velocity.

Optional check At 0, 1, 2 and 3 s, a car moving forwards has velocities of 0, 2, 5 and 9 m/s. Is its acceleration uniform?
At 0, 1, 2 and 3 s, a car moving forwards has velocities of 0, 2, 5 and 9 m/s. Is its acceleration uniform?