Suppose the position function for a free-falling object on a certain planet is given by $s ( t ) = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$. A silver coin is dropped from the top of a building that is 1372 feet tall. Determine the average velocity of the coin over the time interval $[ 3,4 ]$.
A) $- 113 \mathrm { ft } / \mathrm { sec }$
B) $80 \mathrm { ft } / \mathrm { sec }$
C) $112 \mathrm { ft } / \mathrm { sec }$
D) $- 112 \mathrm { ft } / \mathrm { sec }$
E) $- 80 \mathrm { ft } / \mathrm { sec }$

Question

Quizplus · Accepted Answer

The average velocity of the coin over the interval $[3,4]$ is calculated using the formula for average velocity, which is $\frac{s(t_2) - s(t_1)}{t_2 - t_1}$. Given $s(t) = -16t^2 + v_0t + s_0$, with $v_0 = 0$ (since the coin is dropped, not thrown) and $s_0 = 1372$ (the height from which the coin is dropped), we substitute $t_1 = 3$ and $t_2 = 4$ into the position function to find $s(3)$ and $s(4)$, then calculate the average velocity. For $t = 3$, $s(3) = -16(3)^2 + 1372 = -144 + 1372 = 1228$.For $t = 4$, $s(4) = -16(4)^2 + 1372 = -256 + 1372 = 1116$.Thus, the average velocity over the interval $[3,4]$ is $\frac{1116 - 1228}{4 - 3} = \frac{-112}{1} = -112 \, \text{ft/sec}$.

Suppose the Position Function for a Free-Falling Object on a Certain