**AP Physics 1 Question 157: Answer and Explanation**

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**Question: 157**

**7.**

A cart attached to a spring initially moves in the *x* direction at a speed of 0.40 m/s. The spring is neither stretched nor compressed at the cart’s initial position (*x* = 0.5 m). The figure shows a graph of the magnitude of the net force experienced by the cart as a function of *x*, with two areas under the graph labeled. Is it possible to analyze the graph to determine the change in the cart’s kinetic energy as it moves from its initial position to *x* = 1.5 m?

- A. No, the cart’s mass must be known.
- B. Yes, subtract area 2 from area 1.
- C. Yes, add area 2 to area 1.
- D. Yes, determine area 1.

**Correct Answer:** D

**Explanation:**

**D**-The work done by the net force is the area under the graph. Since the cart only moved from position *x* = 0.5 m to *x* = 1.5 m, area 1 is the work done by the net force. By the work-energy theorem, work done by the net force is the change in an object's kinetic energy. (Yes, the mass must be known to determine the values of the initial and final kinetic energy; however, the question asks only for the *change* in kinetic energy.)