In physics, when is an object accelerating?
You've already seen that an object accelerates whenever its velocity changes: speeding up, slowing down, or changing direction. Some motions pack a big velocity change into a short time. Others spread a small change over a long one. This lesson is about judging which of two accelerations is greater.
Cyclist A gains 6 m/s of velocity, from 2 m/s up to 8 m/s, in 4 s. Cyclist B gains the same 6 m/s but takes 8 s. Cyclist A packs the same change into less time, so cyclist A's acceleration is greater.
Cyclist C matches A's 4 s but gains 9 m/s. In the same time, C's velocity changes by more, so C's acceleration is greater than A's.
Cyclist D brakes, losing 6 m/s in 2 s. Losing velocity is a velocity change too. D makes the same size of change as A, in half the time.
The same velocity change in less time means a greater acceleration. So does a bigger velocity change in the same time. The rule holds for speeding up and slowing down alike.
Two cars each take 5 s to speed up. Car P gains 10 m/s of velocity; car Q gains 4 m/s. Which car has the greater acceleration?
Write down the values in the question:
car P: gains 10 m/s in 5 s
car Q: gains 4 m/s in 5 s
Compare the times:
both cars take the same 5 s
Compare the velocity changes:
10 m/s against 4 m/s
Car P has the greater acceleration: its velocity changes by more in the same time.
Speedboat P and speedboat Q each accelerate for the same 4 s. P gains 8 m/s of velocity; Q gains 14 m/s. Which boat has the greater acceleration?
Two runners each slow by 3 m/s near the finish line. Runner R loses it in 2 s; runner S loses it in 6 s. Which runner has the greater acceleration?
Write down the values in the question:
runner R: loses 3 m/s in 2 s
runner S: loses 3 m/s in 6 s
Compare the velocity changes:
both are the same size, 3 m/s lost
Compare the times:
2 s against 6 s
Runner R has the greater acceleration: the same velocity change takes less time.
A greyhound gains 5 m/s of velocity in 2 s. A horse gains 3 m/s of velocity in 4 s. Which animal has the greater acceleration?
Two subway trains brake for the same 6 s. Train A loses 18 m/s of velocity; train B loses 9 m/s. Which train has the greater acceleration?
Two aircraft each slow by 40 m/s after touchdown. The jet takes 20 s; the turboprop takes 50 s. Which aircraft has the greater acceleration?
A loaded freight train and a bicycle each gain 5 m/s of velocity in 10 s. Which has the greater acceleration?