How long (in s) will it take an 875 kg car with a useful power output of 42.0 hp (1 hp = 746 w) to reach a speed of 17.0 m/s, neglecting friction? (assume the car starts from rest.)

The time taken by the car with a useful power output is 4.03 seconds.

Explanation:

Given that,

Mass of the car, m = 875 kg

Initial speed of the car, u = 0

Final speed of the car, v = 17 m/s  

Power of the car, P = 42 hp = 31332 W

The power output of the car is given by the work done per unit time. It is given by :

Initial kinetic energy of the car will be 0 as it is at rest.

Final kinetic energy of the car is :

K = 126437.5

As per the work energy theorem, the change in kinetic energy of the object is equal to the work done.

So,

t = 4.03 seconds

So, the time taken by the car with a useful power output is 4.03 seconds. Hence, this is the required solution.