Question

An automobile of mass m accelerates, starting from rest, with the engine supplying constant power 'P'. How the velocity of the automobile vary with time?

• A.
• B.
• C.
• D. independent of 't'

Answer 1

The correct option is A

As Fv=P=constant
As F = $\frac{mdv}{dt}$
i.e. m$\frac{dv}{dt}$v = P
or
$\int$ vdv =$\int \frac{p}{m}dt$
By integrating both sides we get $\frac{v^2}{2}=\frac{P}{m}t+C_1$
As initially the body is at rest i.e v = 0 at t=0, so $C_1=0\therefore v=(\frac{2Pt}{m}{)}^{\frac{1}{2}}$