## onegirl Group Title 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 one year ago one year ago

1. onegirl Group Title

@SithsAndGiggles can u help?

2. SithsAndGiggles Group Title

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

3. onegirl Group Title

okay

4. onegirl Group Title

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

5. SithsAndGiggles Group Title

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.

6. onegirl Group Title

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

7. SithsAndGiggles Group Title

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.

8. onegirl Group Title

ohh ok

9. onegirl Group Title

so i'm done?