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.
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.
Constant speed along a straight line means zero acceleration. A fast car can have zero acceleration. A slower car gaining speed has non-zero acceleration.