Solve the problem.
-Suppose that a velocity function is given by $v(t)=2 t^{4}$. Find the position function $s(t)$ if $s(0)=7$.
A) $s(t)=\frac{2}{5} t^{5}+7$
B) $s(t)=2 t^{5}+7$
C) $s(t)=\frac{2}{5} t^{5}$
D) $s(t)=8 t^{3}+7$

Question

Quizplus · Accepted Answer

The position function $s(t)$ is the integral of the velocity function $v(t)$. Integrating $v(t) = 2t^4$ gives $s(t) = \frac{2}{5}t^5 + C$. Given $s(0) = 7$, we find $C = 7$. Thus, $s(t) = \frac{2}{5}t^5 + 7$.

Solve the Problem v(t)=2t4v(t)=2 t^{4}v(t)=2t4 Find the Position Function s(t)s(t)s(t) If s(0)=7s(0)=7s(0)=7

Solve the Problem $v(t)=2 t^{4}$ Find the Position Function $s(t)$ If $s(0)=7$