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

$i.e.m\frac{dv}{dt}v=P[AsF=\frac{mdv}{dt}]or\int vdv=\int \frac{p}{m}dt$

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 $C_1=0\therefore v=(\frac{2pt}{m}{)}^{\frac{1}{2}}$