The velocity of an object fired directly upwards given v=96-48t, where t is in seconds. When will the velocity be between 48 and 80 feet per second

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.