(4) (15 Points) A particle moves with acceleration a(t) = 6t - 12 m/s along the s-axis and has initial position and velocity of s(0) = 2 m and v(0) = 9 m/s. (a) Find the velocity and position functions of the particle with proper units. (b) Find the total distance traveled by the particle over the time interval [0,5]. (c) Analyze when the particle is stopped, the time intervals when it is moving forward, backward, speeding up, and/or slowing down for t 0.