Question

When is the instantaneous speed equal to average speed?

Answer 1

Hint: Instantaneous speed is the speed at a certain time and average speed is the mean of all varying speed. These two speeds can be equal when the mean of speeds is the same as the speed throughout the journey. And for the same speed throughout the journey, the body should be in uniform motion.

Complete answer:
Instantaneous speed can be only equal to average speed only when the body is travelling at a uniform speed. In that case the mean of all the speeds will be the same as its constant speed. Instantaneous speed will also be equal to the constant speed of the body. Instantaneous speed is defined as the speed at any certain moment. $$v(t) = {{dx(t)} \over {dt}}$$ . Whereas average speed is defined as the mean of all the speeds during the journey of body $${v_{av}} = {{\sum\limits_N^{i = 1} {{v_i}} } \over N}$$.

Uniform motion of a body is defined as when it travels an equal distance in equal interval of time it is said to be in a uniform motion. for ex- a car travelling with a speed of 40Km/h throughout its journey. There are more types of motion like accelerated motion, non-uniform motion and retarded motion. In practice it is quite difficult to keep the body in uniform motion or constant speed as there are many obstacles in its way. So the instantaneous speed can be equal average speed in only one case, when the body travels with constant speed.

Note: when a body travels with different speed, the average of its speed changes from its current speed. Due to which it does not match with the average speed of its journey. So the body should travel with constant speed to match its instantaneous speed with its average speed. Also speed is a scalar quantity so we cannot take direction into consideration.