Ahoop of mass and radius and a solid cylinder of mass and radius are rolling along level ground with the same translational speed. which object has the greater total kinetic energy?

An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 127 ft at an angle of 31.0° above the horizontal. it then moves 127 ft at an angle of 46.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

What is the final velocity of the initial velocity of 25 and -50?

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1