Particle Motion Project 2) The velocity of a bug traveling along the x-axis is modeled by the function v (t ) = - 2 (t - 1 ) (t - 2) 2 ( t - 4) for t 2 0 where v(t) is measured in meters/hour and t is time in hours. a) Find all time(s) when the bug is at rest. b) On what interval(s) is the bug moving to the left? a c) If #(3) > 0, is the bug speeding up or slowing down at t = 3? Explain your reasoning. d) Does the bug change directions at t = 2? Explain your reasoning.Particle Motion Project A particle moves along the x-axis with position, x(t), graphed below. The position, x(t), is measured in meters and t is time in seconds. O 2 a) Is the particle moving to the right or left at t = 1? Explain your reasoning. b) Is the acceleration of the particle positive, negative, or zero at t = 2.5? Justify your answer. c) Is the particle speeding up or slowing down on the interval 0