Power work energy

Question

The force acting on a particle of mass 1 kg which starts from rest is f = t ^ 3 then the power associated with the particle is proportional to

(A) t ^ 5

(B) t ^ 6

(C) t ^ 7

(D) t ^ 8

Answer 1

power= F.v

F=t^3

F=ma

a=F/m=t^3/1...(here m=1kg)

dv/dt=a....dv=adt...

on integrating both sides

we get v=t^4/4....(keeping the value of a from above)

power= F.v= t^3.t^4/4 = t^7/4...

only proportionality is asked so power is proportional to t^7.

Option C is correct