If the hoist H is moving upward at 6 ft/s, determine the speed at which the motor M must draw in the supporting cable.

The cylindrical cam C is held fixed while the rod AB and bearings E and F rotate about the vertical axis of the cam at a constant rate of = 4 rad/s. If the rod is free to slide through the bearings, determine the magnitudes of the velocity and acceleration of the guide D on the rod as a function of . The guide follows the groove in the cam, and the groove is defined by the equations r = 0.25 ft and z = (0.25 cos ) ft.

A two-stage missile is fired vertically from rest with an acceleration as shown in the graph. In 15 s the first stage A burns out and the second stage B ignites. How fast is the rocket moving and how far has it gone at t = 20 s? How fast is the missile moving and how far has it gone at t = 20 s?

A race car starting from rest moves along a straight track with an acceleration as shown in the graph (where for t 10 s, a = 8 m/s²). Determine the time t for the car to reach a speed of 50 m/s.