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 $\mathrm { t }$.
$$v = \cos \frac { \pi } { 2 } t , s ( 0 ) = 1$$
A) $s = 2 \pi \sin \frac { \pi } { 2 } t$
B) $s = \frac { 2 } { \pi } \sin \frac { \pi } { 2 } t + \pi$
C) $s = \sin t$
D) $s = \frac { 2 } { \pi } \sin \frac { \pi } { 2 } t$ time

Question

Quizplus · Accepted Answer

The position $s(t)$ is found by integrating the velocity function $v(t) = \cos \frac{\pi}{2}t$ with respect to $t$ and then adding the initial position $s(0) = 1$. Integrating $\cos \frac{\pi}{2}t$ gives $\frac{2}{\pi}\sin \frac{\pi}{2}t + C$, where $C$ is the constant of integration. To find $C$, use $s(0) = 1$, which gives $C = 1$. Therefore, the correct expression for $s(t)$ is $s = \frac{2}{\pi}\sin \frac{\pi}{2}t + 1$, but this option is not listed. The closest match, considering the integration process, is option D, acknowledging a mistake in not including the "+1" in the options provided.

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

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