Work, Energy, Power: Accelerating Mass from Rest

[a150daysflood]

Homework Statement

A body of mass m is accelerated uniformly from rest to speed v in time T. The instantaneous power delivered to the body as a function of time is given by?

Homework Equations

P=w/t

e=1/2mv^2

The Attempt at a Solution

P=w/t
P=[0.5m(v/T)^2 ] /t
p=(mv^2) / (tT^2)


Comments:
The answer given is (mv^2)t / (T^2).
Can anyone tell me where i went wrong?

 

[Dale]

P=[0.5m(v/T)^2 ] /t

v/T is not in units of m/s. You should always check your units.

However, I would use a different formula, I would use P = F v. Or, more explicitly for this problem P(t) = F v(t)

 

[Shooting Star]

Just a bit of algebraic jugglery. Let Vf be the final velo, and v the instantaneous velo.

P(t) = Fv = mav = ma^2t, since v=at. But Vf = aT. So, a = Vf/T, which gives,
P(t) = m(Vf/T)^2t.