What describes the relationship between momentum and force according to the laws of motion?

What describes the relationship between momentum and force according to the laws of motion?

• A. The rate of change of momentum is proportional to the force acting on a body and momentum will take place in the direction of the force.
• B. Momentum is independent of force.
• C. Force is proportional to velocity.
• D. Momentum increases with mass independent of force.

Answer: (A)

Momentum changes when a net external force acts on a body, and the rate of that change is what the force does to momentum. This is Newton’s second law in the form F_net = dp/dt. It means the bigger the net force, the faster the momentum changes, and the change happens in the same direction as the force. If the mass is constant, p = m v, so dp/dt = m dv/dt = m a. That shows force is proportional to acceleration and points along it, driving the momentum in that same direction. A larger force over a given time (an impulse) produces a larger increase in momentum, again in the direction of the force. The other statements miss this direct link: momentum isn’t independent of force, force isn’t simply proportional to velocity, and momentum doesn’t just rise with mass regardless of force.

Momentum changes when a net external force acts on a body, and the rate of that change is what the force does to momentum. This is Newton’s second law in the form F_net = dp/dt. It means the bigger the net force, the faster the momentum changes, and the change happens in the same direction as the force.

If the mass is constant, p = m v, so dp/dt = m dv/dt = m a. That shows force is proportional to acceleration and points along it, driving the momentum in that same direction. A larger force over a given time (an impulse) produces a larger increase in momentum, again in the direction of the force.

The other statements miss this direct link: momentum isn’t independent of force, force isn’t simply proportional to velocity, and momentum doesn’t just rise with mass regardless of force.