The equation gives the position s = f(t) of a body moving on a coordinate line (s in meters, t in seconds).
-$$s = - 3 + 7 \cos t$$
Find the body's jerk at time $t = \pi / 3 \mathrm { sec }$.
A) $- \frac { 7 } { 2 } \mathrm {~m} / \mathrm { sec } ^ { 3 }$
B) $- \frac { 7 \sqrt { 3 } } { 2 } \mathrm {~m} / \mathrm { sec } ^ { 3 }$
C) $\frac { 7 \sqrt { 3 } } { 2 } \mathrm {~m} / \mathrm { sec } ^ { 3 }$
D) $\frac { 7 } { 2 } \mathrm {~m} / \mathrm { sec } ^ { 3 }$

Question

Quizplus · Accepted Answer

The jerk is the third derivative of the position function with respect to time. So, we need to find $f'''(t)$.$f(t) = -3 + 7 \cos t$$f'(t) = -7 \sin t$$f''(t) = -7 \cos t$$f'''(t) = 7 \sin t$At $t = \pi / 3$, we have$f'''(\pi / 3) = 7 \sin (\pi / 3) = \frac { 7 \sqrt { 3 } } { 2 }$Therefore, the body's jerk at time $t = \pi / 3 \mathrm { sec }$ is $\frac { 7 \sqrt { 3 } } { 2 } \mathrm {~m} / \mathrm { sec } ^ { 3 }$.

The Equation Gives the Position S = F(t) of a Body