Question

An object has a mass of `4 kg`. The object's kinetic energy uniformly changes from `48 KJ` to `320 KJ` over `t in [0, 12 s]`. What is the average speed of the object?

Answer 1

Average speed is `227.46` `m/s`

Explanation:

Kinetic energy of an objeect of mass `m` kg. moving with a velocity of `v` `m/s` is given by `1/2mv^2` joules. Let the initial velocity is `u` and final velocity be `v`.

As the mass of the object is `4` `kg.` and initial kinetic energy is `48KJ` or `48000J`

We have `1/2xx4xxu^2=48000` i.e. `u^2=24000` and `u=sqrt24000=sqrt(40^2xx15)=40sqrt15=154.92` `m/s`

and as the mass of the object is `4` `kg.` and final kinetic energy is `320KJ` or `320000J`

`1/2xx4xxu^2=320000` i.e. `u^2=160000` and

`v=sqrt160000=400` `m/s`

Hence average speed is `(v+u)/2=(400+154.92)/2=554.92/2=227.46` `m/s`