Answer:
The displac ment between t = 1 and t = 4 is 272 feet
Step-by-step explanation:
To get the displacement of the ball, we first need to get the equation for the position of the ball with respect to time.
We can do this by differentiating the velocity equation given:
v(t) = -32t +96
integrating between the limits of t = 1 and t = 4, we have
[tex]s = \int\limits^4_1 {-32t +96} \, dt[/tex]
[tex]s(t) = -32t^2/2 +96t[/tex]
[tex]s =[ -16t^2 +96t] t = 4, t =1[/tex]
where t = 4.
s = 256 + (96) =352 feet
Where t = 1
s = 80
Displacement of the ball = 352 -80 = 272ft
The displac ment between t = 1 and t = 4 is 272 feet
