The electric motor of a model train accelerates the train from rest to 0.680 m/s in 23.0 ms. The total mass of the train is 580 g. Find the average power delivered to the train during its acceleration.

Answer 1

power = work / time

work = force x distance

force = mass x acceleration

acceleration and distance can be calculated by....

Vf = Vo + at -----> a = (Vf -Vo) / t = Vf/t

and

d = Vot + 1/2 at^2 = 0 + 1/2 * (Vf/t) * t^2 = 1/2 * Vf * t

so....

power = mass x acceleration x distance / t
= m * a * d / t = m * (Vf/t) * (1/2 Vf t) /t = m Vf^2 / (2t)
= 580 g * (.664 m^2/s^2) / (2 * 17 * 10^-3 s) = 17.094 (kg m^2/s^2) / s = 17.094 Joule / sec = 17.094 watts

= 17.1 watts