Displacement of the freely falling body is .

Velocity after a time be .

Velocity is derivative of the displacement with respect to .

Average value of the function on is defined as .

Average velocity with respect to time is defined as

Here .

Average velocity of  is

Velocity at time is .

.

Determine the average velocity with respect to displacement.

Express the velocity function interms of displacement.

Consider .

Displacement function is .

Substiutte   in above expression.

.

Change of integral limits interms of  displacement :

If then .

If then .

Average velocity with respect to time is defined as

Substitute and limits of the integral in above expression.

Velocity at time is .

.

Average velocity with respect to time is .

Average velocity with respect to time is .