NCERT Class 11 Physics Solutions: Chapter 3 – Motion in a Straight Line Part 8

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Question: 3.15

In Exercises 3.13 and 3.14, we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?

Answer:

  • Instantaneous velocity is given by the first derivative of distance with respect to time i.e.,

  • Here, the time interval dt is so small that it is assumed that the particle does not change its direction of motion. As a result, both the total path length and magnitude of displacement become equal is this interval of time.

  • Therefore, instantaneous speed is always equal to instantaneous velocity.

Image shows the instantaneous velocity

Image Shows the Instantaneous Velocity

Question: 3.16

Look at the graphs (a) to (d) (Fig.) carefully and state, with reasons, which of these cannot possibly represent one - dimensional motion of a particle

A)

Graph shows the one-dimensional motion

Graph Shows the One-Dimensional Motion - A

B)

Graph shows the one-dimensional motion

Graph Shows the One-Dimensional Motion - B

C)

Graph shows the one-dimensional motion

Graph Shows the One-Dimensional Motion - C

D)

Graph shows the one-dimensional motion

Graph Shows the One-Dimensional Motion - D

Answer:

  • The given graph, shown in (a), does not represent one-dimensional motion of the particle. This is because a particle cannot have two positions at the same instant of time.

  • The given graph, shown in (b), does not represent one-dimensional motion of the particle. This is because a particle can never have two values of velocity at the same instant of time.

  • The given graph, shown in (c), does not represent one-dimensional motion of the particle. This is because speed being a scalar quantity cannot be negative.

  • The given graph, shown in (d), does not represent one-dimensional motion of the particle. This is because the total path length travelled by the particle cannot decrease with time.