A car is moving along a straight road. The graph below shows how the speed
varies with time.
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Which of the following graphs represents the distance covered by the car with
time?
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To determine the graph that represents the distance covered by the car with time, we need to keep in mind the relationship between speed, time, and distance.
The graph of speed vs. time shows how the speed of the car changes with time. The speed represents how fast the car is moving at any given moment.
To find the distance covered by the car, we need to calculate the area under the graph of speed vs. time. The area under the graph represents the distance traveled.
Let's analyze each of the given graphs to see which one represents the distance covered by the car with time:
Graph 1: t
This graph represents time on the x-axis, and there is no information about speed or distance. Therefore, it does not represent the distance covered by the car with time.
Graph 2:
This graph represents speed on the y-axis and time on the x-axis. It shows a constant speed of the car over time. Since the area under the graph (represented by the shaded region) is a triangle, it represents the distance covered by the car during that time.
Graph 3:
This graph also represents speed on the y-axis and time on the x-axis. It shows a decrease in speed over time, indicating that the car is slowing down. Since the area under the graph (represented by the shaded region) is a trapezoid, it also represents the distance covered by the car during that time.
Graph 4:
This graph represents speed on the y-axis and time on the x-axis. It shows an increase in speed over time, indicating that the car is speeding up. Since the area under the graph (represented by the shaded region) is a triangle, it also represents the distance covered by the car during that time.
Based on the analysis, graphs 2, 3, and 4 represent the distance covered by the car with time.