13. (II) The force on a particle, acting along the x axis, varies as shown in Fig. 6-38.Determine the work done by this force to move the particle along the x axis:(a) from x=0.0 to x=10.0m (b) from x=0.0 to x=15.0 FIGURE 6-38 Problem 13.

To determine the work done by the force to move the particle along the x-axis, we need to calculate the area under the force vs. displacement graph between the specified limits of x. The work done by a force is given by the integral of the force with respect to displacement, which geometrically corresponds to the area under the force-displacement curve.Given the turning points and the shape of the graph, we can divide the graph into trapezoids and triangles to calculate the area.(a) From m to m:The graph increases linearly from (0,0) to (0,350), then remains constant at 350 N from (0,350) to (15,350). To find the work done from m to m, we only need to consider the area under the graph from m to m.This area is a right triangle with a base of 10.0 m (from 0 to 10 m) and a height of 350 N. The area of a right triangle is given by: Plugging in the values: So, the work done by the force to move the particle from m to m is 1750 J.(b) From m to m:For this part, we need to consider the entire area under the graph from m to m. This includes the triangle from part (a) and a rectangle from m to m.The area of the rectangle is given by: Adding this to the work done from part (a): So, the work done by the force to move the particle from m to m is 3500 J.Final answers:(a) The work done from m to m is 1750 J.(b) The work done from m to m is 3500 J.