3. a roller coaster car sits at rest at the top of a hill, 23.5 meters tall. what will be the final
velocity of the car at the bottom of the hill?

If the material fails when the average normal stress reaches 120 psi, determine the largest centrally applied vertical load p the block can support.

Find the absolute value of the change of the gravitational potential energy (gpe) of the puck-earth system from the moment the puck begins to move to the moment it hits the spring. use 0.253 m for the displacement of the puck along the ramp and 9.80 m/s2 for the acceleration due to gravity. assume that the mass of the puck is 0.180 kg.

Aparticle's position is given by x = 6.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".