Question

Body of mass m accelerates uniformly from rest to v in time t.As function of x instantaneous power delivered to body is

Answer 1

we have

v = u + at

now, as u = 0 and t = T1

a = v/T1

so, force

F = ma = m(v/T1)

now,

we also have

s = ut + (1/2)at2

as u = 0

s = (1/2)at2 = (1/2) (v/T1).t2

and work done will be

W = F.s = m(v/T1) .(1/2) (v/T1).t2

or

W = (1/2).m.(v/T1)2.t2

and finally the instantaneous power will be

P = W/t = [(1/2).m.(v/T1)2.t2] / t

thus,

P = (1/2).m.(v/T1)2.t

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