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onegirl
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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
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

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onegirl Group TitleBest ResponseYou've already chosen the best response.0
@SithsAndGiggles can u help?
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.0
\[v(t)=s'(t),\text{ so }\int v(t)~dt+C=s(t)\] So the first thing you do find the indefinite integral of the given \(v(t)\): \[\int(40\sin t)~dt\]
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.0
ok so s(t) = 40t + cos(t) + c = 40(0) + cos(0) + c = 2
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.0
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.
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.0
so i should plug in 2 into 40t + cost + c right? and okay
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.0
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.
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.0
so i'm done?
 one year ago
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