Solve the problem.
-The equation for free fall at the surface of Planet $X$ is $s = 4.16 t ^ { 2 } \mathrm {~m}$ with $t$ in seconds. Assume a rock is dropped from the top of a $600 \mathrm {~m}$ cliff. Find the speed of the rock at $t = 5 \mathrm { sec }$.
A) $42.6 \mathrm {~m} / \mathrm { sec }$
B) $41.6 \mathrm {~m} / \mathrm { sec }$
C) $19.8 \mathrm {~m} / \mathrm { sec }$
D) $20.8 \mathrm {~m} / \mathrm { sec }$

Question

Quizplus · Accepted Answer

To find the speed of the rock at $t = 5$ seconds, we differentiate the given equation $s = 4.16t^2$ with respect to $t$ to get the velocity as a function of time, $v(t) = ds/dt = 2 \cdot 4.16 \cdot t = 8.32t$. Substituting $t = 5$ seconds into $v(t) = 8.32t$ gives $v(5) = 8.32 \cdot 5 = 41.6 \mathrm{~m/s}$.

Solve the Problem XXX Is s=4.16t2 ms = 4.16 t ^ { 2 } \mathrm {~m}s=4.16t2 m

Solve the Problem $X$ Is $s = 4.16 t ^ { 2 } \mathrm {~m}$