OK so we need to find the function v(t) which will tell us where the particle is at any given time.
We know that the derivative of distance is speed and the derivative of speed is acceleration.
In this case we need to work backwords and find the integrals.
a(t) = 13 sin(t) + 4 cos(t)
s(t)= integral of above = 13(-cos(t)) + 4(sin(t)) + C
v(t)= integral of above = -13sin(t) -4cos(t) +Ct + D
Now I believe you have incorrect initial conditions
s(0) = 0, s(2π) = 10
As cos and sin functions have the same value at 0 and 2Pi the above cannot be true.
My guess is that one is s(0) and the other is v(2Pi) or the other way round.
These initial conditions will determine the value of the two constants: C and D.
Hope this helps.
