A car is pushed along a long road that is straight, horizontal, and parallel to the x direction.

a)The horizontal force on the car varies with x as shown in the figure. What is the work done on the car by this force? (Let a = 100 N.) _____J
b)What is the work done by gravity on the car? _____J

To calculate the work done on the car by a force, we use the formula:

Work = Force × Distance × cos(θ)

a) To find the work done on the car by the horizontal force, we need to calculate the area under the force vs. distance graph shown in the figure.

The area under a force vs. distance graph represents the work done by the force. In this case, since the force varies with x, we need to calculate the area under each segment of the graph.

The graph shows a triangular shape with a base of 100 N and a height of 500 m. The area of a triangle is given by:

Area = (1/2) × base × height

Therefore, the work done on the car by the horizontal force is:

Work = (1/2) × 100 N × 500 m = 25,000 J

So, the work done on the car by the horizontal force is 25,000 J.

b) To find the work done by gravity on the car, we need to consider the vertical component of the displacement. Since the road is horizontal, the vertical component of displacement is zero, and therefore, the work done by gravity is also zero.

So, the work done by gravity on the car is 0 J.