Take, the acceleration due to gravity 10 ms^-2.

A car of mass 500 kg has a maximum speed of 40 m/s on a level road with the engine of the car working at a constant power of 20 kW. The resistance to motion is proportional to the square of the speed.

a. Find the acceleration when the speed is 20 m/s.

b. Find the distance traveled with the speed increases from 20 m/s to 30 m/s.

c. When the car reaches the speed 30 m/s, the power is switched off. Find the time required to reduce the speed from 30 m/s to 20 m/s.