A particle moves along a straight line. For 0 <= t <= 5, the position of the particle is given by s(t) = 3t + 4t^2 - t^3 What is the average velocity of the particle over the interval 0 <= t <= 4?
Find a general expression for the velocity of the particle as a function of time, v(t), and determine the value of v at t=2. Is the particle traveling to the left or the right at this point? Justify your answer.
Find all times t during the interval 0 <= t<= 5 that the particle changes direction. Justify your answer.
At t = 4, is the speed of the particle increasing or decreasing? Justify your answer