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?

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Answer 1 · 2016-04-16T02:41:21

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

(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#