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

Question

Quizplus · Accepted Answer

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

Solve the Problem t\mathrm { t }t v=8πsin⁡4tπ,s(π2)=2\mathrm { v } = \frac { 8 } { \pi } \sin \frac { 4 \mathrm { t } } { \pi } , \mathrm { s } \left( \pi ^ { 2 } \right) = 2v=π8​sinπ4t​,s(π2)=2

Solve the Problem $\mathrm { t }$ $\mathrm { v } = \frac { 8 } { \pi } \sin \frac { 4 \mathrm { t } } { \pi } , \mathrm { s } \left( \pi ^ { 2 } \right) = 2$