Solve the problem.
-Suppose that an object's acceleration function is given by $a(t)=10 t+6$. The object's initial velocity, $v(0)$, is 3 , and the object's initial position, $s(0)$, is 12 . Find $s(t)$.
A) $\frac{10}{3} t^{3}+3 t^{2}+12 t+3$
B) $\frac{5}{3} t^{3}+3 t^{2}+3 t+12$
C) $5 t^{2}+6 t+3$
D) $\frac{5}{3} t^{3}+3 t^{2}+3 t$

Question

Quizplus · Accepted Answer

To find $s(t)$, integrate the acceleration function $a(t) = 10t + 6$ to get the velocity function $v(t)$. Then integrate $v(t)$ to find the position function $s(t)$. Use the initial conditions $v(0) = 3$ and $s(0) = 12$ to solve for the constants of integration.

Solve the Problem a(t)=10t+6a(t)=10 t+6a(t)=10t+6 the Object's Initial Velocity v(0)v(0)v(0) , Is 3 , and the Object's Initial Position

Solve the Problem $a(t)=10 t+6$ the Object's Initial Velocity $v(0)$ , Is 3 , and the Object's Initial Position