Question

The acceleration of a particle is
a(t) = −18 sin3t 0 ≤ t ≤ 8
(a) If v(0) = 6 and x(0) = 4, find v(t) and x(t). (b) At what times is the particle farthest from the origin

Answer 1

x'=v
v'=a
so
you integrate a to find v (apply the v(0)=6 to find the constant of integration)

then integrate v to find x (apply the x(0)=4 to find the constant of integration)