The position of a particle moving along an x axis is given by x = 16.0t - 3.00t, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 4.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at what time is it reached? (h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (i) Determine the average velocity of the particle between t = 0 and t = 4,00 s.

A person on an icy expedition is trying to lower a crate of mass m1 = 5.65 kg crate to the bottom of a steep ravine of height h2 21.8 m using a rope over a simple pulley. The person, who m2 frictionless %| weighs m2 = 60.9 kg, is being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point h = 12.1 meters above the ground, the person slips and the crate immediately accelerates toward the ground, dragging the hapless person across the ice and toward the edge of the cliff. h If we assume the ice is perfectly slick (that is, no friction between the person and the ice once he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff. speed: m/s At what speed will the person hit the bottom of the ravine? (Assume no air friction.) speed: m/s

7. An arrow of mass 0.018 kg is shot upward at an angle from the ground, reaching a maximum height of 25 m with a speed of 62 m/s. Neglecting air resistance, with what speed will the arrow hit the ground?

A bowling ball is dropped from the top of a building that has a height of h = 112 m. Part (a)  Assuming air resistance is negligible, what is the ball's speed, vf in m/s, when it strikes the ground?Part (b)  If drag produces an opposing force of 10 N while the ball's falling, what is the ball's speed, vf in m/s, when it strikes the ground? Assume the ball has a mass of 5 kg.Part (c)  A different ball was dropped and the final speed was measured to be vf = 8.5 m/s while the drag force was measured to be 50 Newtons. What is the mass of this ball in kg?