The acceleration of a particle is defined by the relation a 52kv2.5, where k is a constant. the particle starts at x 5 0 with a velocity of 16 mm/s, and when x 5 6 mm, the velocity is observed to be 4 mm/s. determine (a) the velocity of the particle when x 5 5 mm, (b) the time at which the velocity of the particle is 9 mm/s.

Consider a small frictionless puck perched at the top of a fixed sphere of radius r. if the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere? [hint: use conservation of energy to find the puck's speed as a func e conservation of energy to find the puck's speed as a function of its height at what value of this normal force does the puck leave the sphere? ] here on the puck.