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Solve the problem.
-If an object is thrown straight upward from the ground with an initial speed of 112 feet per second, then its height, $h$, in feet after $t$ seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 112 t$. Find the instantaneous speed of the object at $t = 6$
A) $112 \mathrm { ft } / \mathrm { sec }$
B) $- 464 \mathrm { ft } / \mathrm { sec }$
C) $- 80 \mathrm { ft } / \mathrm { sec }$
D) $16 \mathrm { ft } / \mathrm { sec }$

Question

Quizplus · Accepted Answer

To find the instantaneous speed of the object at $t = 6$, we need to differentiate the given height equation with respect to time $t$ to get the velocity equation, $v(t) = \frac{dh}{dt}$. Differentiating $h(t) = -16t^2 + 112t$ gives $v(t) = -32t + 112$. Substituting $t = 6$ into $v(t)$ gives $v(6) = -32(6) + 112 = -192 + 112 = -80$ ft/sec.

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