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The following figure gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at points A, B, C and D?
The following figure gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at points A, B, C and D?
CBSE | Class 11 | Motion in a Straight Line | NCERT | Physics
The following figure gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at points A, B, C and D?

The slope of the particle’s speed-time graph provides information on the particle’s acceleration. The slope of the graph in the specified interval determines the magnitude of the particle’s average acceleration.

The graph’s slope in interval 2 is the highest and is in a negative direction. As a result, it has the greatest average acceleration magnitude.

The average speed, on the other hand, is determined by the particle’s speed magnitude. The average speed will be determined by the magnitude of the speed because the time intervals are nearly identical. Because the particle’s speed is highest in interval 3, it will have the highest average speed.

The signs of speed are positive at all intervals, whereas the acceleration is determined by the graph’s slope.
Because the slope of the interval 1 is positive, the acceleration is positive.
Since the slope of the interval 2 is negative, the acceleration is negative.
Since slope of the interval 3 is positive, the acceleration is positive.

At the four instants A,B,C, and D, the slope of the speed-time graph is parallel to the time axis. It means that the graph’s slope is zero. As a result, the particle’s acceleration will be 0 at these points.

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