A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P_0. The instantaneous velocity of this car is proportional to

A car of mass m starts from rest and accelerates so that the instantan

1.	A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P_0. The instantaneous velocity of this car is proportional to
Answer» `t^2 P_0` `t^(1//2)` `t^(-1//2)` `t/(sqrtm)` SOLUTION :`P_0 = Fv :. F = ma = m(dv)/(dt)` `:. P_0 = mv (dv)/(dt) " or " P_0dt = mvdv` INTEGRATING both SIDES, we get `int_(0)^(t) P_0 dt = m int_0^vvdv , P_0t = (mv^2)/(2) , v = ((2P_0t)/(m))^(1//2)` or `v PROP sqrt(t)`.