onegirl 2 years ago 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

1. onegirl

@SithsAndGiggles can u help?

2. SithsAndGiggles

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

3. onegirl

okay

4. onegirl

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

5. SithsAndGiggles

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

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

7. SithsAndGiggles

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

ohh ok

9. onegirl

so i'm done?