Question

the graph above shows the velocity v as a function of time t for an object moving in a straight line. which of the following graphs shows the corresponding displacement x as a function of time t for the same time interval?

Explanation:

Step1: Recall the relationship between velocity and displacement

The slope of the displacement - time graph gives the velocity. When the velocity is zero, the displacement - time graph has a horizontal slope. When the velocity is positive and constant, the displacement - time graph has a positive and constant slope (a straight - line with positive slope). When the velocity is increasing, the slope of the displacement - time graph is increasing (concave up), and when the velocity is decreasing, the slope of the displacement - time graph is decreasing (concave down).

Step2: Analyze the velocity - time graph segments

In the first segment of the velocity - time graph, the velocity is increasing from zero to a positive value. So, the displacement - time graph should be concave up. In the second segment, the velocity is constant. So, the displacement - time graph should be a straight line with a positive slope. In the third segment, the velocity is decreasing to zero. So, the displacement - time graph should be concave down.

Step3: Evaluate each option

Option (A): The graph starts with a straight - line segment instead of a concave - up segment for the increasing velocity part, so it is incorrect.
Option (B): This graph has the correct shape. It starts concave up for the increasing velocity part, then has a straight - line segment for the constant velocity part, and then is concave down for the decreasing velocity part.
Option (C): The graph does not have a straight - line segment for the constant velocity part, so it is incorrect.
Option (D): The graph does not have a concave - down part for the decreasing velocity part, so it is incorrect.
Option (E): The graph does not have a straight - line segment for the constant velocity part, so it is incorrect.

Answer:

B.