Please see the link http://people.westminstercollege.edu/faculty/ccline/courses/phys211/hw-f07/hw-211-u10.pdf question # 10-8)

The center of mass of a cart having a mass of 0.62 kg starts with a velocity of -2.5 m/s along an x-axis. It starts from a position of 5 m and moves without any friction towards the position of 0 m.

A fan assembly on the cart is operated such as to push it with variable force. From a position of 5 m to 3 m, the force increases linearly from 0 to 0.5 N. From the position of 3 m to 1 m, the force decreases linearly to 0.2 N and remains constant over the final 1 m.

The work done on the cart by the air being expelled by the fan is equal to:

`int_0^2 (0.5/2)*x dx + int_0^2 (0.2 + 0.3/2*x) dx + 0.2*1`

=` 0.25*(2^2 - 0^2)/2 + 0.2*(2 - 0) + .15*(2^2 - 0)/2 + 0.2`

= 0.25*2 + 0.4 + 0.3 + 0.2

= 0.5 + 0.4 + 0.3 + 0.2

= 1.4

The work done by the air expelled by the fan is equal to 1.4 J