Question

The figure below gives the acceleration of a 1.75 kg parade as it is moved from rest along an x axis by an applied force F_a, from x = 0 to x = 9 m. The scale of the figure's vertical axis is set by a_S = 5.5 m/s^2. How much work has the force done on the particle when the particle reaches the following points? x = 5 m x = 8 m x = 9 m What is the particle's speed and direction of travel when it reaches each of the following points? x = 5 m x = 8 m x = 9 m

Answer 1

work done = force * distance

force = mass * acceleration

work done = mass * acceleration * distance

acceleration * distance is taken out by area of the graph

area of the graph till x = 5 m

area = 0.5 * 5.5 * 1 + 5.5 * 3 + 0.5 * 5.5 * 1

work done = 1.75 * (0.5 * 5.5 * 1 + 5.5 * 3 + 0.5 * 5.5 * 1)

work done = 38.5 J

when distance is 8 m

area = 0.5 * 5.5 * 1 + 5.5 * 3 + 0.5 * 5.5 * 1 - 0.5 * 5.5 * 1 - 5.5 * 2

work done = 1.75 * (0.5 * 5.5 * 1 + 5.5 * 3 + 0.5 * 5.5 * 1 - 0.5 * 5.5 * 1 - 5.5 * 2)

work done = 14.4375 J

when distance is 9 m

work done = 1.75 * (0.5 * 5.5 * 1 + 5.5 * 3 + 0.5 * 5.5 * 1 - 0.5 * 5.5 * 1 - 5.5 * 2 - 0.5 * 5.5 * 1)

work done = 9.625 J