Barron's 2nd Edition DT Q34

Barron's Book

34) This problem asks us to find the work done on the mass by a variable force. Normally, we would just solve for work using W = F*d. However, that won't work for this problem since the force is variable. Instead, we will use a different method.

If you have never taken a calculus class, you probably won't understand the red equation. Essentially, it means you are taking the area between a force(F) vs. displacement(x) curve and the x-axis.

Be careful! This only works with a force versus displacement graph.

Since the graph makes the shape of a triangle, we will simply use the formula for the area of a triangle.

Where F is force, d is displacement, A is area, b is base length, and h is height

Since the area between the curve and the x-axis is 15, our work done by the variable force will be 15 Joules.

Answer: C