Question

a ball is shot straight upward. with it's height, in feet, after t seconds given by the function f(t)=-16t^2+192t. Find the average velocity of the ball from t=1 to t=6

Answer 1

`80 {ms}^( - 1)`

Step-by-step explanation

The average velocity of the ball is the rateof displacement over the total time.

The height of the ball, in feet, after t seconds is given by the function:

`f(t)=-16t^2+192t`

At time t=1, the height of the ball is

`f(1)=-16(1)^2+192(1)`

`f(1)=-16+192 = 176ft`

At time t=6, the height of the ball is

`f(6)=-16(6)^2+192(6)`

`f(6)=-16(36)+192(6)`

`f(6)=-576+1152 = 576`

The average velocity

`= (f(6) - f(1))/(6 - 1)`

`= (576- 176)/(6 - 1)`

`= (400)/(5)`

`= 80 {ms}^( - 1)`