A particle is moving with the given data. find the position of the particle. at) = 12 sin (t) + 7 cos (t), s (0) = 0, s (2π) = 18

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Madalyn Wells

Mathematics

16 January, 20:22

A particle is moving with the given data. find the position of the particle. at) = 12 sin (t) + 7 cos (t), s (0) = 0, s (2π) = 18

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Dolce · Answer 1

v (t) is the integral of a (t), so v (t) = - 12 cos (t) + 7 sin (t) + c (where c is a constant) s (t) is the integral of v (t), so s (t) = - 12 sin (t) - 7 cos (t) + ct + d (where d is a constant) Solving s (0) = 0 gives d = 7. Solving s (2pi) = 18 gives c = 9/pi. So the position is s (t) = - 12 sin (t) - 7 cos (t) + 9t/pi + 7.