Choose the one alternative that best completes the statement or answers the question.
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 $s ( t ) = - 16 t ^ { 2 } + 112 t + 4$ 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 $v(t) = s'(t) = -32t + 112$. Plugging in $t = 0.5$ seconds into the velocity function gives $v(0.5) = -32(0.5) + 112 = -16 + 112 = 96$ feet per second.

Choose the One Alternative That Best Completes the Statement or Answers