Question

a cart starts from rest and moves to the right along a flat surface. the velocity of the cart as a function of time is represented in the graph. which of the following quantities are the same for both segments a and segment b of the graph?
a acceleration
b displacement
c elapsed time
d average velocity

Explanation:

Step1: Recall acceleration - velocity graph relation

Acceleration is the slope of the velocity - time graph. Since the slopes of segments A and B are different, acceleration is not the same.

Step2: Recall displacement - velocity graph relation

Displacement is the area under the velocity - time graph. The areas under segments A and B are different, so displacement is not the same.

Step3: Analyze elapsed time

The time intervals for segments A and B are different, so elapsed time is not the same.

Step4: Recall average - velocity formula

Average velocity $\bar{v}=\frac{\Delta x}{\Delta t}$. For a velocity - time graph, if we consider the start and end points of each segment, we can find that the average velocity can be the same. For example, if segment A has a lower maximum velocity but a longer time interval and segment B has a higher maximum velocity but a shorter time interval, the ratio of displacement (area under the curve) to time interval can be equal for both segments.

Answer:

D. Average velocity