Question

If the average velocity is non-zero for some time interval,
does this mean that the instantaneous velocity is never zero
during this interval?explain

Answer 1

May not. The instantaneous velocity at any point among this time interval can be zero even the average velocity is non - zero.

We know that average velocity is the change in position divided by the time interval, but instantaneous velocity indicates the velocity attained at a particular point of time during motion.

The expression for average velocity is,

$\displaystyle\sf {v_{av}=\dfrac {x_2-x_1}{t_2-t_1}}$

Then,

$\displaystyle\sf {v_{av}\neq0\implies x_1\neq x_2}$

So there's change in position. But there should be too many possible positions between $\displaystyle\sf {x_1}$ and $\displaystyle\sf {x_2}$ at any of which the velocity can be zero too, since $\displaystyle\sf {t_2-t_1}$ is not at all an infinitesimally small difference.

An example is given. Consider a bus travelling on a road so that it has an average velocity for a particular time interval. But if the bus is brought to a stop at any point during this time interval then the instantaneous velocity of the bus at this point is zero.

Thus the average velocity of a body being non - zero doesn't make sense that its instantaneous velocity can never be zero during the considered time interval.