Question

the motion of an object moving along a straight line is described by the acceleration versus time graph in figure 1. a student claims that the motion of the object can also be represented by the velocity versus time graph in figure 2. which of the following correctly states whether or not the student’s claim is true and explains why? a no, because the object’s speed is increasing, the acceleration should be positive. b no, because the object’s speed is increasing, the acceleration should be increasing in magnitude. c yes, because the area under the curve of the acceleration versus time graph could represent a negative velocity that would be increasing in magnitude. d yes, because the slope of the graph of acceleration versus time is constant, so the velocity of the object approaches a constant value. answer b incorrect. the rate that the acceleration changes does not determine whether the velocity will increase or decrease. the sign of the acceleration indicates how the velocity changes.

Explanation:

The area under the acceleration - time graph gives the change in velocity. In Figure 1, the acceleration is negative and increasing in magnitude over time. The area under this curve can represent a negative velocity that is increasing in magnitude as shown in Figure 2. Option A is wrong because a negative acceleration can still lead to an increase in speed if the velocity is also negative. Option B is incorrect as the increase in speed is related to the sign of acceleration, not the rate of change of acceleration magnitude. Option D is wrong because a constant - slope acceleration - time graph does not mean the velocity approaches a constant value; rather, it means the rate of change of acceleration is constant.

Answer:

C. Yes, because the area under the curve of the acceleration versus time graph could represent a negative velocity that would be increasing in magnitude.