Solve the problem.
-time Given the velocity and initial position of a body moving along a coordinate line at time $t$, find the body's positios $\mathrm { t }$.
$$v = - 19 t + 8 , s ( 0 ) = 8$$
A) $s = - 19 t ^ { 2 } + 8 t + 8$
B) $s = \frac { 19 } { 2 } t ^ { 2 } + 8 t - 8$
C) $s = - \frac { 19 } { 2 } t ^ { 2 } + 8 t + 8$
D) $s = - \frac { 19 } { 2 } t ^ { 2 } + 8 t - 8$

Question

Quizplus · Accepted Answer

We integrate the given velocity function to get the expression for position: 
\begin{align*}
\int v\, dt &= \int (-19t+8)\, dt \
s(t) &= -\frac{19}{2}t^2 +8t +C
\end{align*}
Using the initial condition $s(0)=8$, we can solve for the constant $C$:
\begin{align*}
s(0) &= -\frac{19}{2}(0)^2 +8(0) +C \
8 &= C \
\end{align*}
Therefore, the position function is given by $s(t)=-\frac{19}{2}t^2+8t+8$, which is choice $\boxed{	extbf{(C)}}$.

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

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