A ball is thrown vertically upward with an initial velocity of 128 feet per second, the ball’s height after t second is s(t) = 128t – 16t². Find the instantaneous velocity at 4 seconds.
v(t) = ds/dt = 128-32t
So, plug in t=4.
To find the instantaneous velocity at a specific time, we need to find the derivative of the position function with respect to time. In this case, since the position function is given as s(t) = 128t - 16t^2, we can find the derivative and plug in the value of t to get the instantaneous velocity.
The derivative of s(t) with respect to t will give us the velocity function, denoted as v(t).
Let's find the derivative of s(t):
s'(t) = d/dt (128t - 16t^2)
To differentiate the function, we apply the power rule and constant rule:
s'(t) = 128 - 32t
Now, let's find the instantaneous velocity at t = 4 seconds.
Plug in t = 4 into the velocity function:
v(4) = 128 - 32(4)
= 128 - 128
= 0
Therefore, the instantaneous velocity at 4 seconds is 0 feet per second.