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)P_(0)`
B. `t^(1//2)`
C. `t^(-1//2)`
D. `(t)/(sqrt(m))`

Answer

B

Explanation

Constant power of car, `P_(0)=F(upsilon)`
`=ms(upsilon)=m(dupsilon)/(dt)(upsilon)` or`P_(0)dt=m upsilon d upsilon`
Integrating both sides, we get
`int_(0)^(t)P_(0)dt=int_(0)^(upsilon)m upsilond upsilon=(m upsilon^(2))/(2), i.e., P_(0)(t)=(m upsilon^(2))/(2)`
`upsilon=sqrt((2P_(0)(t))/(m))` or `upsilon prop t^(1//2)`