1. The problem statement, all variables and given/known data The force on a particle, acting along the x axis, varies as shown in the figure below. (a) Determine the work done by this force to move along the x-axis from x=0.0 to x = 10.0m and (b) from x=0.0 to x=15.0m and (c) what is the speed of the particle at each slope change and x-intercept. (graph of force applied in the x-direction vs distance attached - please ignore all pencil markings, those are a part of a different discussion). 2. Relevant equations W=F x d (work = force x distance) W=PE + KE (work = potential energy + kinetic energy) PE = mgh (potential energy = mass times gravity times height) KE = (1/2)mv^2 (kinetic energy = 1/2 times mass times velocity squared PE initial + KE initial = PE final + KE final (conservation of energy) 3. The attempt at a solution For part (a) and (b), I found the areas under or above the red line - that was fairly straightforward, BUT the professor added in his own part (c), that being to find the speed of the particle at each slope change and x-intercept. I am certain the solution to part (c) has something to do with the conservation of energy. I thought maybe the total work done on and by the particle would cancel each other out, and therefore I can set the conservation of energy equation to zero and solve for particle speed, and the mass (which is not given) would simple cancel out, but since the amount of work done on and by the particle are different areas on the graph, they don't cancel each other out. Therefore, I am left with two unknowns in my equation, that being the velocity and the mass. There is another equation I am not considering, I am sure of it.