Question

please help me work through this or at least part, I thought i understood, but i need help!

Answer 1

Solution

Step 1:

Write the equation for the distance function:

$v(t)\text{ = -cost + 3sint + 3}$

Step 2:

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Part 1

$\begin{gathered} v(t)\text{ = -cost + 3sint + 3} \\ \\ \frac{ds(t)}{dt}=−cost+3sint+3 \\ \\ ds(t)=(−cost+3sint+3)dt \\ \\ s(t)=\int(−cost+3sint+3)dt \\ \\ s(t)\text{ = -sint - 3cost + 3t + c} \\ \\ s(0)\text{ = -sin\lparen0\rparen - 3cos\lparen0\rparen + 3\lparen0\rparen + c} \\ c\text{ = 3} \end{gathered}$

Find s(t), if s(0) = 0

s(t) = -sint - 3cost + 3t + 3

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Part 2

$\begin{gathered} v(t)\text{ = -cost + 3sint + 3} \\ \\ a(t)\text{ = }\frac{dv(t)}{dt} \\ \\ \frac{dv(t)}{dt}\text{ = sint + 3cost} \\ \\ a(t)\text{ = sint + 3cost} \end{gathered}$

Find a(t)

a(t) = sint + 3cost