<h2>
a) Initial velocity = 83 ft/s</h2><h2>
b) Object's maximum speed = 99.4 ft/s</h2><h2>
c) Object's maximum displacement = 153.64 ft</h2><h2>
d) Maximum displacement occur at t = 2.59 seconds.</h2><h2>e)
The displacement is zero when t = 5.70 seconds</h2><h2>
f) Object's maximum height = 153.64 ft</h2>
Explanation:
We have velocity
v(t)= -32t + 83
Integrating
s(t) = -16t²+83t+C
At t = 0 displacement is 46 feet
46 = -16 x 0²+83 x 0+C
C = 46 feet
So displacement is
s(t) = -16t²+83t+46
a) Initial velocity is
v(0)= -32 x 0 + 83 = 83 ft/s
Initial velocity = 83 ft/s
b) Maximum velocity is when the object reaches ground, that is s(t) = 0 ft
Substituting
0 = -16t²+83t+46
t = 5.70 seconds
Substituting in velocity equation
v(t)= -32 x 5.70 + 83 = -99.4 ft/s
Object's maximum speed = 99.4 ft/s
c) Maximum displacement is when the velocity is zero
That is
-32t + 83 = 0
t = 2.59 s
Substituting in displacement equation
s(2.59) = -16 x 2.59²+83 x 2.59+46 = 153.64 ft
Object's maximum displacement = 153.64 ft
d) Maximum displacement occur at t = 2.59 seconds.
e) Refer part b
The displacement is zero when t = 5.70 seconds
f) Same as option d
Object's maximum height = 153.64 ft
