Question

This is a velocity versus time graph of a car starting from rest. If the area under the line is 10 meters, what is the corresponding time interval? A. 2 seconds B. 4 seconds C. 5 seconds D. 10 seconds E. 15 seconds

Answer 1

The time interval corresponding to the area under the velocity-time graph, find the area under the curve, which represents the displacement of the car. In this case, the area under the line is 10 meters, so the corresponding time interval is 2 seconds.

To determine the time interval corresponding to the area under the velocity-time graph, you need to find the area under the curve, which represents the displacement of the car. Since the car starts from rest, the area under the velocity-time graph represents the displacement of the car during that time interval. In other words, the area is equal to the distance traveled by the car. You mentioned that the area under the line is 10 meters.

Therefore, the corresponding time interval can be found by examining the options. Let's check the options:

A. 2 seconds: If the time interval is 2 seconds,

The area (1/2) * base * height = (1/2) * 2 * 10 = 10 square meters.

This matches the given area. So, the correct answer is A. 2 seconds.

Answer 2

The corresponding time interval is 5 seconds.

Step-by-step explanation:

The area under the velocity versus time graph represents the displacement of an object. In this case, the area is 10 meters. To calculate the corresponding time interval, we need to divide the area by the average velocity. If the car started from rest, its initial velocity is 0 m/s.

If we assume the car's velocity is constant during this time interval, the average velocity is simply the final velocity, which is 10 m/s, divided by 2 (since the car starts from rest). Therefore, the corresponding time interval is 5 seconds (10 meters divided by 2 m/s).