(3-7)
① work = force x distance travelled = 2 x (40 – 10) = 2N x 30m = 60 J
This is the area under the line on the graph, between these two limits.
② Since the dependence of force on distance is linear, the mean force applied over the range between 10m and 40 m distance is just the force at the midpoint of this range
= 2.5 N
So work = force x distance = 2.5 x 30 = 75 J. You can easily verify that this is again equal to the area under the line in this range.
③ we just add up the areas of each slice: (10 x 3.5) + (10 x 2.5) + (10 x 1.5) = 75 J.