Question

If a rocket with a mass of `900` `"tons"` vertically accelerates at a rate of `3` `ms^-2`, how much power will the rocket have to exert to maintain its acceleration at `4` seconds?

Answer 1

The power exerted by the rocket at `t=4` `s` is `32.4` `MW`.

Explanation:

(I am assuming that the question means metric (SI) tonnes (1000 kg), not imperial tons (1016 kg))

The velocity at `t=4` `s` is:

`v=u+at=0+3*4=12` `ms^-1`

Now there's a little bit of a sequence to work through.

Work: `W=Fd`

Power: `P=W/t=(Fd)/t=Fd/t`

but `v=d/t`, so `P=Fv`

To find the force being exerted, we use Newton's Second Law:

`F=ma`, so:

`P=mav=900000*3*12=32,4000,000` `W=32.4` `MW`