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 cars velocity as a function of time, in terms of P, t, and m

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, youd 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)