Prove that S=ut+1/2at^2

While goofing off at the ice skating rink, a student takes off her shoes and places each of them on the ice. her friend, a hockey player, then shoots a hockey puck at each shoe. the first puck immediately comes to rest after it collides with the left shoe. the second puck rebounds after it collides with the right shoe. if each hockey puck has the same incoming speed, which shoe has greater speed after the collision? the right shoe. both shoes have the same speed. the left shoe.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)

An object resting on a table weighs 100 n. with what force is the object pushing on the table? with what force is the table pushing on the object? explain how you got your answer.