Find the position function s(t) from the given velocity or acceleration function and initial value(s). Assume that units are feet and seconds. v(t) = 40 – sin t, s(0) = 2

Question

Find the position function s(t) from the given velocity or acceleration function and initial value(s).  Assume that units are feet and seconds. v(t) = 40 – sin t, s(0) = 2

anonymous · Answer

@SithsAndGiggles  can u help?

anonymous · Answer

$$v(t)=s'(t),\text{ so }\int v(t)~dt+C=s(t)$$
So the first thing you do find the indefinite integral of the given $v(t)$:
$$\int(40-\sin t)~dt$$

anonymous · Answer

okay

anonymous · Answer

ok so s(t) = 40t + cos(t) + c = 40(0) + cos(0) + c = 2

anonymous · Answer

Yeah, that looks right, but when you write it out you have two separate equations: the first being the more general $s(t)=40t+\cos t+C$ and the second involving the initial values, $s(0)=40(0)+\cos 0+C=2$.

Anyway, solving for C and plugging it into the first equation gives you your answer.

anonymous · Answer

so i should plug in 2 into 40t + cost + c right?  and okay

anonymous · Answer

No, you have that $s(0)=2$, so you would just plug in 0 for t and set the equation equal to 2. You had it right, but you should have written that step in another equation.

anonymous · Answer

ohh ok

anonymous · Answer

so i'm done?