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

Power `p_(0) = Fv = (m(dv)/(dt)) v = mv (dv)/(dt)`
Integrating both sides
`int p_(0) dt = int mv dv implies p_(0)t = (mv^(2))/(2)`
`v^(2) =(2 p_(0) t)/(m) implies v prioop t^(1//2)`