Solve the problem.
-A foul tip of a baseball is hit straight upward from a height of 4 feet with an initial velocity of 112 feet per second. The function $$s ( t ) = - 16 t ^ { 2 } + 112 t + 4$$ 4 describes the ball's height above the ground, s(t), in feet, t seconds
After it was hit. What is the instantaneous speed of the ball 0.5 seconds after it was hit?
A) -28.8
B) 96
C) -67.2
D) 28.8

Question

Quizplus · Accepted Answer

The instantaneous speed of the ball 0.5 seconds after it was hit can be found by taking the derivative of the height function $s(t) = -16t^2 + 112t + 4$ with respect to time $t$ to get the velocity function $v(t) = -32t + 112$, and then substituting $t = 0.5$ into this velocity function. Doing so gives $v(0.5) = -32(0.5) + 112 = -16 + 112 = 96$ feet per second. This represents the speed of the ball at that instant, indicating that choice B is correct.

Solve the Problem s(t)=−16t2+112t+4s ( t ) = - 16 t ^ { 2 } + 112 t + 4s(t)=−16t2+112t+4

Solve the Problem $s ( t ) = - 16 t ^ { 2 } + 112 t + 4$