The position of a point particle is given by the function x(t) = 4-6t+(5/2)t^2-(1/3)t^3, where x is in meters and t is in seconds.
(a) Determine the equation for velocity of the particle as a function of time. Create a graph of velocity vs. time for the particle, for the time interval 0 <= t <= 5s.
(b) Determine the equation for the acceleration of the particle as a function of time. Create a graph of acceleration vs. time for the particle, for the time interval 0 <= t <= 5s.
(c) Describe, in natural language, the motion of this particle for the time interval 0 <= t <= 5s. Be sure to include in your answer:
1. time intervals when the particle is speeding up or slowing down
2. times when the particle changes direction
(d) Determine the distance traveled by and the displacement of the particle for the time interval 0 <= t <= 5s.
(e) If the particle has a mass of 2.0kg, determine a function for the net force on the particle as a function of time.
(f) Determine the impulse imparted to this particle during the time interval 0 <= t <= 5s.
(g) Determine the work done by the net force on the particle during the time interval 0 <= t <= 5s.