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?

Question

Philoid · Accepted Answer

Instantaneous velocity is defined as first derivative of distance with respect to time, v_in = m/s

The time interval dt is very small such that direction particle doesn’t change. Since, velocity and speed differ in direction only.

Thus,

Instantaneous velocity = Instantaneous speed ……always