A force acting on a particle varies with x as shown in Figur

A force acting on a particle varies with x as shown in Figure 6.8. Calculate the work done by the force on the particle as it moves from x = 0 to x = 6.0. The force acting on a particle is constant for the first 4.0 m of motion and then decreases linearly with x from x_= 4.0 m to x = 6.0 m.

Solution

Work done = area under Force vs displacement curve

So, the shaded area will give our answer

We see the area is comprised of a rectangular portion between x = 0m to x= 4m and a triangular portion between x = 4 to x = 6m,

area of the rectangular portion = 5*4 = 20 J

area of the triangular portion = 0.5*2*5 = 5 J

So, total area = net work done = 20 +5 = 25 J <--------answer