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Given acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a = 10cos5t ; v(0) = -6 ; s(0) = 12

Mathematics
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integrate a(t) from 0 to t the constant of integration will be v(0) integrate again from 0 to t the constant of integration will be s(0)
It seems take you forever to understand the purpose of initial values :/ V(t) = ∫ a(t) dt = 2sin 5t + C V(0) = 2 sin 0 + C = - 6 -> C = -6 =>S(t) = ∫ v(t)dt = ∫ (2sin5t -6 ) dt = .... + C S(0) = 12 -> C = ...

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