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?

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Solution

The instantaneous speed is always equal to the magnitude of the instantaneous velocity because for very small instants of time the length of the path is equal to the magnitude of displacement.

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Similar questions

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?

Q. Statement 1: Magnitude of average velocity is equal to average speed.
Statement 2: Magnitude of instantaneous velocity is equal to instantaneous speed.

Q. Statement - 1 : In a given time interval, the average speed of a particle may be equal to magnitude of average velocity.
Statement - 2 : The magnitude of instantaneous velocity is equal to instantaneous speed of a particle in motion.

Q. When a particle moves with variable velocity, which of the following relations are false?
(I) Average speed = average velocity
(II) Instantaneous speed = instantaneous velocity
(III) Distance covered = magnitude of displacement

Q. Can a body have
a.Zero instantaneous velocity and yet be accelerating?
b.Zero average speed but non-zero average velocity?
c.Negative acceleration and yet be speeding up?
d.The magnitude of average velocity be equal to average speed?

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