Question

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 1

Hey buddy,

# Reason-
a) Instantaneous velocity is given by the first derivative of distance with respect to time
v = dx / dt
b) Instantaneous speed is given by limit of average speed when dt tends to 0.
v' = lim(average speed), dt→0

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.

Therefore, instantaneous speed is always equal to instantaneous velocity.

Hope I helped...

Answer 2

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Instantaneous velocity. The rate of change of displacement of an object in a particular direction is its velocity.The magnitude of instantaneous velocity equals the instantaneous speed. This happens because, for an infinitesimally small time interval, the motion of a particle can be approximated to be uniform.