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 .