The velocity function is
v(t) = 96 - 48t
where v is in ft/s
t is in seconds.
When v = 48 ft/s, obtain
96 - 48t = 48
48 = 48t
t = 1
When v = 80 ft/s, obtain
96 - 48t = 80
-48t = -16
t = 1/3
The velocity is between 48 and 80 ft/s when t is between 1 and 1/3 seconds.
The velocity of 80 ft/s is attained first at 1/3 seconds, and the velocity of 48 ft/s is attained later at 1 second.
The graph illustrates the answer.
Answer: Between 1/3 and 1 second.
