Integration Word Problem?

Question

A particle moves along the x-axis so that, at any time t>=0 acceleration is given by a(t) = 6t + 6. At time t = 0, the velocity of the particle is -9, and its position is -27.

a. Find v(t), the velocity of the particle at any time t>=0

b. For what values of t >= 0 is the particle moving to the right?

c. Find x(t), the position of the particle at any time t >= 0

Thanks, I appreciate it.

Answer 1

a. Just integrate a(t) to get v(t), then plug 0 in for x to solve for C.

b. If it's moving to the right, velocity is positive.  Simple Increase/decrease problem.

c. Integrate v(t), which you found earlier, and plug in 0 for x to solve for C.