The position of a particle is given by the equation 5 = f (t) = t3 27::2 + 240t (6 pts.) Where t is measured in seconds and s in centimeters. (a) Find the velocity at time t. What is the velocity after ls? (b) When is the particle at rest? (c) When is the particle moving in the positive direction, when is the particle moving in the nega' ((1) Draw a diagram to represent the motion of the particle. (c) Find the total distance traveled by the particle during the rst 15 seconds. (1) Find the acceleration at time t and after 10 seconds