How long will it take the falling object, initially at rest, falling due to gravity, to reach an instantaneous velocity of 96 feet per second?

Question

How long will it take the falling object, initially at rest, falling due to gravity, to reach an instantaneous velocity of 96 feet per second?

____ seconds.

Answer 1

Start with the fact that the acceleration due to gravity is a constant 32 ft/s² at the Earth's surface:

Then, realizing that acceleration is the derivative of velocity:

When t = 0, then the velocity at that time can be considered the initial velocity. So, C = v_i (initial velocity)

Therefore v(t) = v_i - 32t

Since, in this case the initial velocity is zero (it is at rest), and we know that the instantaneous velocity is -96 (negative because it's going downwards) then:

-96 = 0 - 32t

t = -96/-32 = 3 seconds