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 $\mathrm { t }$.
$v = - 5 t + 3 , s ( 0 ) = 12$
A) $s = - \frac { 5 } { 2 } t ^ { 2 } + 3 t + 12$
B) $s = \frac { 5 } { 2 } t ^ { 2 } + 3 t - 12$
C) $s = - 5 t ^ { 2 } + 3 t + 12$
D) $s = - \frac { 5 } { 2 } t ^ { 2 } + 3 t - 12$

Question

Quizplus · Accepted Answer

The position $s(t)$ is found by integrating the velocity function $v(t) = -5t + 3$. Integrating gives $s(t) = -\frac{5}{2}t^2 + 3t + C$. Given $s(0) = 12$, we find $C = 12$, so $s(t) = -\frac{5}{2}t^2 + 3t + 12$.

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

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