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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

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  1. onegirl
    • 2 years ago
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    @SithsAndGiggles can u help?

  2. SithsAndGiggles
    • 2 years ago
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    \[v(t)=s'(t),\text{ so }\int v(t)~dt+C=s(t)\] So the first thing you do find the indefinite integral of the given \(v(t)\): \[\int(40-\sin t)~dt\]

  3. onegirl
    • 2 years ago
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    okay

  4. onegirl
    • 2 years ago
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    ok so s(t) = 40t + cos(t) + c = 40(0) + cos(0) + c = 2

  5. SithsAndGiggles
    • 2 years ago
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    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
    • 2 years ago
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    so i should plug in 2 into 40t + cost + c right? and okay

  7. SithsAndGiggles
    • 2 years ago
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    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
    • 2 years ago
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    ohh ok

  9. onegirl
    • 2 years ago
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    so i'm done?

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