# Is instantaneous speed always equal to the magnitude of instantaneous velocity?

Is instantaneous speed always equal to the magnitude of instantaneous velocity? What about the infinitesimal time duration when the direction changes? How can it ALWAYS be equal?

This is due to the fact that for a small interval of time the distance is approximately the same as displacement. Just like in a curve, when we zoom into it small change in position is actually the distance covered. When divided by the same time change "$$dt$$" the magnitudes of the rates of change of displacement and distance which are velocity and speed respectively are equal.

Hope that helps! The direction of instantaneous velocity at any time gives the direction of motion of a particle at that point in time. 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.

• Why downvote for correct answer? – Anusha Jul 1 at 5:49

Instantaneous speed is defined as the magnitude of instantaneous velocity. They are equal by definition.

Perhaps you are thinking of the magnitude of instantaneous acceleration, and the rate of change of speed, which are not equal in general.