Let a(t), v(t) and s(t) be the acceleration, velocity, and position functions respectively of a particle. If a(t)=5cos(t/2)+sint and s(0)=0, v(0)=-5. How do i find the position function s(t)??

Question

find s(t) as the second integral of a(t)

s(t)= INTINT a(t) dt dt
= INT (10sint/2 -cost + c)dt
= - 20cost/2 - sint + ct + k where c, k are consttants.
Now evaluate v(0) to find c, and s(o) to find c.