$\"\"$

The Position function is $\"\"$ and the time interval is $\"\"$ .

The velocity is defined as rate of change of position with respect to time $\"\"$ in the interval $\"\"$ is

$\"\"$ .

The velocity in the interval $\"\"$ :

$\"\"$

Average velocity is $\"\"$ .

$\"\"$

Find instantaneous velocity at $\"\"$ .

Instantaneous velocity is the derivative of the position function with respect to $\"\"$ .

Consider the Position function is $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Substitute $\"\"$ in the above function.

Instantaneous velocity $\"\"$ .

Hence the average velocity in the interval $\"\"$ is same as instantaneous velocity at $\"\"$ .

$\"\"$

Average velocity is $\"\"$ .

Instantaneous velocity $\"\"$ .

The average velocity in the interval $\"\"$ is same as instantaneous velocity at $\"\"$ .