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An object of 5 kg is moving initially at 4 m/s in the positive x direction. At time t=0, it is acted upon by a force F=(4t+1) N in the positive x direction. What is the velocity of the object at t=5 s?

What is the potential energy associated with a conservative force F(x)=3x^2-1? Please draw the graph of U(x) in your supporting work. Is there a stable equilibrium point for this potential energy?

As in the previous problem, a uniform rod of mass M and length L is pivoted at one end. At L/4 from the other end, a point mass m is attached to the rod. The system is held horizontally. As the rod is let go, find the angular velocity of the system at the moment of passing the vertical position.

A solid disk is mounted so it can rotate without friction about an axis through its center. Initially, it rotates with some angular velocity ω0{“version”:”1.1″,”math”:”ω0″}. A second disk, initially not rotating, is dropped concentrically onto the disk. The second disk has the same mass and half the radius of the first disk. When the two come to a common rotation, what is the final angular velocity?

A body is moving in the positive x direction while being acted upon by a net force. The graph of the net force as a function of the body’s position is represented in the figure below. When the body is at x=0, its speed is 20 m/s. At which of the marked points is the speed of the body the closest to 20 m/s?

A uniform rod of mass M and length L is pivoted at one end. At L/4 from the other end, a point mass m is attached to the rod. The system is held horizontally. As the rod is let go, find the initial angular acceleration of the system.

A body of mass 10 kg is initially at rest on a horizontal surface. The coefficient of static friction between the body and the surface is 0.7, and the coefficient of kinetic friction is 0.4. A horizontal force 50 N is applied to the body. What is the friction force acting on the body?

A uniform solid sphere starts from rest and rolls down the inline of height h. What is the speed of the center of mass of the sphere at the bottom of the incline?

Consider the Atwood machine in the figure below. If the pulley is massless and m1=3m2{“version”:”1.1″,”math”:”m1=3m2″}, what is the magnitude of the acceleration of the system?

An object is displaced by r → = ( 5 m ) i ^ − ( 2 m ) j ^ {“version”:”1.1″,”math”:”\vec{r}=(5\,m)\hat{i}-(2\,m)\hat{j}”} while it is acted upon by  F → = − ( 8 N ) i ^ + ( 22 N ) j ^ . {“version”:”1.1″,”math”:”\vec{F}=-(8\, N)\hat{i}+(22\,N)\hat{j}.”}What is the work done on the object by this force?