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Numerade Educator

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Problem 62 Hard Difficulty

A particle is moving with the given data. Find the position of the particle.

$ a(t) = 3\cos t - 2\sin t $, $ \quad s(0) = 0 $, $ \quad v(0) = 4 $

Answer

$$
s(t)=2 \sin t-3 \cos t+2 t+3
$$

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Video Transcript

For this problem, we're starting off with an acceleration function. Three co sign t minus two. T f t equals three. Sign t minus two. Okay, that means that our velocity function is going to be the anti derivative of those. So we're going to end up getting three sign T plus to co sign antique. Classy. But we know that via zero is four. So based on that, we see that C is going to be too. Then we want to find the position function as a T I think equal to the anti derivative of these components. So we'll have uh to 70 yeah minus three coats. Mt us to T. That's our constant. Loving to the constant. You get three. So this is our final position function.