power word problem

Question

An athlete's foot is in contact with a kicked football for 100 milliseconds and exerts a force on the football over a distance of 20 centimeters. The force starts at 0 N and increases linearly to 2000 N for 50 milliseconds through a distance of 10 centimeters and then decreases linearly for 50 milliseconds through a distance of 10 centimeters. What is the average power of the athlete's foot while it is in contact with the ball?

Answer 1

Power is average work divided by total time

Work is average force times distance.

Calculations assume meters and seconds are the units used

For this problem the average force in the first half of the contact is 1000 newtons. The average force for the second half is also 1000 newtons. The total average work is therefore 1000 newtons times the distance applied (20cm), therefore 1000N time 0.2 meters = 200 joules. The power is then calculated by dividing the work by the total time (100 milliseconds or 0.1 sec.)

So, average power = 200 joules/0.1 sec = 2000 watts