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Numerade Educator

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Problem 63 Hard Difficulty

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

$ a(t) = 10\sin t + 3\cos t $, $ \quad s(0) = 0 $, $ \quad s(2\pi) = 12 $

Answer

$$
s(t)=-10 \sin t-3 \cos t+\frac{6}{\pi} t+3
$$

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Video Transcript

okay. Remember that acceleration is the derivative of lost piece of lost ease, the integral or anti derivative of acceleration. They're for V. A T. Thea anti derivative would be negative co signed t with three sign of tea, plus our constant A. You can also give it C or D. Any name really works and then position is the integral velocity. It's a night of signed team, as three co signed t plus a our first constant times TV Plus B, which is our second constant. Now we know as of 00 therefore us of zero, we can play again plus eight times zero plus b said equal to zero. This gives us b is equivalent to three and remember us of two pious 12 so passive to pie his negative ton sign to pie here minus three co sign to pa for us too. Hi plus three is equivalent to 12. Therefore, to pie eh equals 12 therefore is equivalent to sex over pi. Therefore, a final equation is us of cheese is negative. 10 cider T minus three co sign of tea Put six over pi T plus three