Question

An object has a mass of `2 kg`. The object's kinetic energy uniformly changes from `135 KJ` to `36KJ` over `t in [0, 6 s]`. What is the average speed of the object?

Answer 1

I found `9.2m/s`

Explanation:

We need the speed of the object at each instant so we can use the definition of Kinetic Energy `K=1/2mv^2` to find it:
`K_i=1/2mv_i^2`
and
`K_f=1/2mv_f^2`

using our data:
`135=1/2*2v_i^2`
`v_i=11.6m/s`

and

`36=1/2*2v_f^2`
`v_f=6m/s`

we can now use:
`v_f=v_i+at`
and find `a`:
`6=11.6+6a`
`a=-0.9m/s^2`
we now use:
`v_f^2=v_i^2+2as`
to find the distance:
`36=135-2*0.9*s`
`s=55m`
So:
`"average speed"="distance"/"time"=s/t=55/6=9.2m/s`