Solve the problem.
-Given the velocity and initial position of a body moving along a coordinate line at time $t$, find the body's positios $\mathrm { t }$.
$v = \frac { 8 } { \pi } \sin \frac { 4 t } { \pi } , s \left( \pi ^ { 2 } \right) = 2$
A) $s = - 2 \cos \frac { 4 t } { \pi } + 4$
B) $s = - 2 \cos \frac { 4 t } { \pi } + 8.2134$
C) $s = 2 \cos \frac { 4 t } { \pi } + 4$
D) $s = - 2 \cos \frac { 4 t } { \pi } + 3.3073$ time

Question

Quizplus · Accepted Answer

The position function $s(t)$ is found by integrating the velocity function $v(t)$. Integrating $v = \frac{8}{\pi} \sin \frac{4t}{\pi}$ gives $s(t) = -2 \cos \frac{4t}{\pi} + C$. Using the initial condition $s(\pi^2) = 2$, we solve for $C$ and find $C = 4$. Thus, $s(t) = -2 \cos \frac{4t}{\pi} + 4$.

Solve the Problem ttt , Find the Body's Positios t\mathrm { t }t

Solve the Problem $t$ , Find the Body's Positios $\mathrm { t }$