Question

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?

Class XI Physics Motion In A Straight Line Page 57

Answer 1

Hello !
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The average velocity and average acceleration can be different or same 
But instantaneous speed is equal to the instantaneous velocity because in this instantaneous we have to find the speed or velocity at a particular time in which they cant be different 

Answer 2

Instantaneous speed of the particle at an instant is the first derivative of the distance with respect to time at that instant of time i.e v(ins)=dx/dt.

Since in instantaneous speed we take only a small interval of time (dt) during which direction of motion of a body is not supposed to change, hence there is no difference between total path length and magnitude of displacement for small interval of time dt. Hence, instantaneous speed is always equal to magnitude of instantaneous velocity.