Question

An object has a mass of `6` `kg`. The object's kinetic energy uniformly changes from `88` `kJ` to `48` `kJ` over `t in [0, 6 s]`. What is the average speed of the object?

Answer 1

From the kinetic energy and the mass given, the initial speed is `5.4` `ms^-1` and the final speed is `4` `ms^-1`. The average speed is `4.7` `ms^-1`.

Explanation:

I don't think we actually need to know the time taken. Let's find out.

We know `E_k=1/2mv^2`, which we can rearrange to give:

`v=sqrt(2E_k/m)`

That means the initial speed (we don't care about direction) is:

`v=sqrt(2E_k/m)=sqrt(2xx(88)/6)~~5.4` `ms^-1`

The final speed is:

`v=sqrt(2E_k/m)=sqrt(2xx(48)/6)=4` `ms^-1`

Since the object is decelerating uniformly, the average speed will just be:

`(v_"initial"+v_"final")/2 = (5.4+4)/2 = 4.7` `ms^-1`

Whether it decelerated over 1, 2 or 6 seconds, the average speed would be the same.