A body is thrown on a rough surface such that the friction force acting on it is linearly varying with the distance travelled by it as `f=ax+b`. Find the work done by the friction on the box if before coming to rest the box travels a distance s.

Explanation

As the force is acting in the direction opposite to the motion of the box, work done by this force must be negative. As force is not constant, we use
`W=-underset0oversetsintintfdx=-underset0oversets int(ax+b)*dx=((ax^2)/(2)+bx)_0^s`
`=-1/2as^2-bs`