Neco 2017 Physics Question 49

A particle moves in a straight line. Its velocity-time graph is as follows: from \(t=0\,\text{s}\) to \(t=4\,\text{s}\) the velocity increases uniformly from \(0\,\text{m s}^{-1}\) to \(8\,\text{m s}^{-1}\); from \(t=4\,\text{s}\) to \(t=6\,\text{s}\) the velocity remains constant at \(8\,\text{m s}^{-1}\); from \(t=6\,\text{s}\) to \(t=8\,\text{s}\) the velocity decreases uniformly to \(0\,\text{m s}^{-1}\). During the same interval a force-displacement graph for the particle shows a straight line starting at the origin \((0\,\text{m}, 0\,\text{N})\) and reaching a force of \(10\,\text{N}\) at a displacement of \(24\,\text{m}\). Assuming the only other horizontal force is kinetic friction, determine the work done by friction over the whole \(8\,\text{s}\) interval. Give your answer in joules (signed).