NCERT Class 11 Physics Solutions: Chapter 3 – Motion in a Straight Line Part 11

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Question: 3.21

Figure gives the x-t plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which interval is the average speed greatest, and in which is it the least? Give the sign of average velocity for each interval.

One-dimensional motion in graph

One-Dimensional Motion in Graph

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Answer:

  • Interval 3 (Greatest), Interval 2 (Least)

  • Positive (Intervals 1 & 2), Negative (Interval 3)

  • The average speed of a particle shown in the x-t graph is obtained from the slope of the graph in a particular interval of time.

  • It is clear from the graph that the slope is maximum and minimum restively in intervals 3 and 2 respectively. Therefore, the average speed of the particle is the greatest in interval 3 and is the least in interval 2. The sign of average velocity is positive in both intervals 1 and 2 as the slope is positive in these intervals. However, it is negative in interval 3 because the slope is negative in this interval.

Question: 3.22

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 the points A, B, C and D?

Graph shows the speed - time

Graph Shows the Speed - Time

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Answer:

  • Average acceleration is greatest in interval 2 Average speed is greatest in interval 3 v is positive in intervals 1, 2, and 3 a is positive in intervals 1 and 3 and negative in interval 2 a = 0 at A, B, C, D

  • Acceleration is given by the slope of the speed-time graph. In the given case, it is given by the slope of the speed-time graph within the given interval of time.

  • Since the slope of the given speed-time graph is maximum in interval 2, average acceleration will be the greatest in this interval.

  • Height of the curve from the time-axis gives the average speed of the particle. It is clear that the height is the greatest in interval 3. Hence, average speed of the particle is the greatest in interval 3.

In interval 1:

  • The slope of the speed-time graph is positive. Hence, acceleration is positive.

  • Similarly, the speed of the particle is positive in this interval.

In interval 2:

  • The slope of the speed-time graph is negative. Hence, acceleration is negative in this interval.

  • However, speed is positive because it is a scalar quantity.

In interval 3:

  • The slope of the speed-time graph is zero. Hence, acceleration is zero in this interval. However, here the particle acquires some uniform speed. It is positive in this interval.

  • Points A, B, C, and D are all parallel to the time-axis. Hence, the slope is zero at these points. Therefore, at points A, B, C, and D, acceleration of the particle is zero.