Question

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

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.