$\"\"$

The height of an object after $\"\"$ sec is $\"\"$ .

(a)

Find the average velocity of the $\"\"$ over $\"\"$ .

The average velocity is $\"\"$ .

$\"\"$

Therefore the average velocity of the object is $\"\"$ .

$\"\"$

(b)

The function $\"\"$ is continuous over closed interval $\"\"$ , and differentiable on the open interval $\"\"$ .

Therefore mean value theorem can be applied.

So, there exists at least one number $\"\"$ in $\"\"$ such that $\"\"$ .

$\"\"$

Apply derivative with respect to $\"\"$ .

$\"\"$

So $\"\"$ .

$\"\"$

Therefore from the Mean Value Theorem at $\"\"$ sec, the instantaneous velocity equals the average velocity.

$\"\"$

The average velocity of the object is $\"\"$ .

The time where instantaneous velocity equals the average velocity is $\"\"$ sec.