A 650 g bird is stuck on the upper free end of a vertical spring with a spring constant of 14 N/m. The bottom of the ideal spring is tied to the earth. The bird trying to liberate itself from the spring flies vertically at a time t = 0 s, producing a constant vertical force of 12 N. The spring has been stretched 64 cm at time t. Determine the speed of the bird at time t.

A 5.0 kg bucket of water resting on a horizontal surface is tied to a vertical rope. The rope of negligible mass passes through a frictionless pulley. The other end of the rope is attached to a 6.0 kg weight. The weight is dropped from a height of 2.5 m. Find the speed of the weight just before it hits the floor.

A 2.5 kg object is initially at rest at position s = 5.0 m on a potential energy diagram given by U(s) = -2s³ + 4s² J. Determine the object's velocity when it reaches position s = 8.0 m.

A toboggan is initially pushed up a friction-free slope set at a 17.0° angle, achieving a height of 1.23 m above its launch point. Determine its initial speed.

A 10.0-kg dog slides down a ramp 2.30 m high and arrives at the bottom from a stationary start, moving at 1.40 m/s. Determine the quantity of thermal energy generated by friction in this action.

A toy car of mass 1.5 kg is positioned at the top of a frictionless ramp (KL), depicted in the diagram below. The next part of the track is a horizontal span (LM) measuring 5.0 m with a coefficient of kinetic friction of 0.35. The subsequent section, MN, features a frictionless segment where a damping device is located. The car, initially stationary at point K, is released to traverse the track. Upon reaching point M, the car activates the damping device causing it to compress. Determine the velocity of the car at point M if the velocity of the car at point L is 6.2 m/s.

A toy truck, with a mass of 1.8 kg, is released from rest from the top of a sand hill as illustrated below. Upon reaching point Y, the toy truck compresses the spring-like device by 0.15 m. Calculate the stiffness constant k for the spring-like device if the velocity of the truck at point Y is 3.5 m/s and the portion YZ is frictionless.