Step 1 :

(a)

The height of the ball after t seconds is .

Initial velocity of the ball at the surface of the Moon .

The average velocity of ball at time t is \ \

Velocity is derivative of displacement function.

Differentiate s(t) with respect to t.

Velocity of ball after t seconds is .

Velocity of ball after 2 seconds

Velocity of ball after 2 seconds is 14.76 m/s.

Step 1 :

(a)

The height of the ball after t seconds is .

Initial velocity of the ball at the surface of the Moon .

The average velocity of ball at time t is \ \

The average velocity of ball at time 2 is \ \

\ \

So the average velocity formula at t = 2 is

Step 2 :

(b)

The average velocity for the time interval beginning when t = 2 with duration 1 seconds .

Substitute in average velocity formula .

The average velocity for the time interval beginning when t = 2 with duration 0.5 seconds .

Substitute in average velocity formula .

The average velocity for the time interval beginning when t = 2 with duration 0.05 seconds .

Substitute in average velocity formula .

Step 3 :

From the above calculations [ part (b) ] , one can estimate the instantaneous velocity at t = 2 .

When the duration of time decreases , the instantaneous velocity approaches to 14.7 m/s .

Check :

The instantaneous velocity at t = 2 is

Solution :

(a) the average velocity formula at t = 2 is .

(b) The average velocity when t = 2 with duration 1 seconds is .

     The average velocity when t = 2 with duration 0.5 seconds is .

     The average velocity when t = 2 with duration 0.5 seconds is .

(c) The instantaneous velocity at t = 2 is .