On a frictionless horizontal surface, an initially stationar...

Question

On a frictionless horizontal surface, an initially stationary object is subjected to a constant horizontal force F. After a time t, the object's momentum is p, and its kinetic energy is . If the object starts from rest and remains under the influence of the same force F, what will the object's momentum and kinetic energy be after a time 2t?

To solve this problem, we need to understand the relationship between force, momentum, and kinetic energy over time.

Momentum:

Momentum is given by the equation:

If the force is constant and the object starts from rest, the momentum increases linearly with time.

After time , the momentum is . After time , the momentum will be:

So, the momentum after time is 2p, not .

Kinetic Energy:

Kinetic energy is given by the equation:

Using Newton’s second law and the fact that the velocity is , we can express the kinetic energy as:

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