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

Options

A. `t^2 P_0`
B. `t^(1//2)`
C. `t^(-1//2)`
D. `t/(sqrtm)`

Answer

B

Explanation

`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^v vdv , P_0t = (mv^2)/(2) , v = ((2P_0t)/(m))^(1//2)` or `v prop sqrt(t)`.