Which statement correctly describes how momentum changes when velocity doubles while mass remains constant?

Which statement correctly describes how momentum changes when velocity doubles while mass remains constant?

• A. It quadruples
• B. It remains the same
• C. It halves
• D. It doubles

Answer: (D)

Momentum is mass times velocity, so with mass held constant, momentum changes in direct proportion to velocity. Doubling velocity doubles momentum because you’re multiplying the same mass by twice as large a velocity. For example, a 3 kg object speeding from 4 m/s to 8 m/s has momentum that goes from 12 kg·m/s to 24 kg·m/s. The momentum would quadruple only if velocity increased by a factor of four, and it would stay the same if velocity didn’t change or halve if velocity were cut in half.

Momentum is mass times velocity, so with mass held constant, momentum changes in direct proportion to velocity. Doubling velocity doubles momentum because you’re multiplying the same mass by twice as large a velocity. For example, a 3 kg object speeding from 4 m/s to 8 m/s has momentum that goes from 12 kg·m/s to 24 kg·m/s. The momentum would quadruple only if velocity increased by a factor of four, and it would stay the same if velocity didn’t change or halve if velocity were cut in half.