A car of mass `m` starta from rest and accelerates so that the instyantaneous power delivered to the car has a constant magnitude `P_(0)`. The instaneous velocity of this car is proportional to

Options

A. `t^(2)`
B. `t^(1//2)`
C. `t^(-1//2)`
D. `(t)/(sqrt(m))`

Answer

B

Explanation

Constant power of car `P_(0)`=F.V=ma.v
`P_(0)m(dv)/(dt).v`
`P_(0)`dt=mvdc Integrating
`P_(0)t=(mv^(2))/(2) v=sqrt((2P_(0)t)/(m))`