Question

A car, which is accelerating uniformly from rest, travels a distance of 28.5 m in the tenth second of its motion. What is its acceleration?

The only thing I can think of is to use v=u+at, where u = 0 m/s, t = 10 s and v = 28.5 m/s. But the velocity is constantly increasing so the final velocity value is incorrect. Hmm.

Answer 1

The acceleration is `"3 m/s"^2`.

Explanation:

Let the acceleration of the car be `a`. The initial velocity will obviously be `"0 m/s"` as the car was at rest. Putting this into Newton's Second Law of Motion, we get

`0 * 10 + 1/2 * a * 10^2 -(0 * 9 + 1/2 * a * 9^2)=28.5`

`=> 50a-40.5a=28.5`

`=> a=3`

To find the distance traveled in the 10th second, we have to subtract the total distance traveled in `9` seconds from the total distance traveled in `10` seconds.