A car of mass m accelerates from rest along a level straight track, not at constant acceleration but with constant engine power, P . Assume that air resistance is negligible. a) Find the car's velocity as a function of time, in terms of P , t , and m

Question

A car of mass m  accelerates from rest along a level straight track, not at constant acceleration but with constant engine power, P . Assume that air resistance is negligible.   a) Find the car's velocity as a function of time, in terms of P , t , and m

anonymous · Answer

Because P = W ÷ t, and W = F*t, you can substitute (W) for (F*t). Then substitute (F) for (m*a). This will leave you with P = (m*a*d)/t. Since you need velocity, you'd want to solve for "a" so you can use v = a*t.      a = (P*t)/(m*d)   therefore, substituting "a" in v = a*t,   v = (P*t*t)/(m*d)