Question

If the engine of a car of mass m is capable of power P, the minimum time needed for the car to accelerate from rest to a speed v is?

Answer 1

Determine the force:

$$F=2P/v,\\\space\\ ma=F,\\\space\\ ma=2P/v,\\\space\\ a=\frac{2P}{mv}.$$

The time:

$$t=v/a=\frac{mv^2}{2P}.$$