Which of the following objects requires the greatest change in $p$ (momentum) in order to stop its motion?

• A. A $20\mathrm{kg}$ sled moving at $1m/s$
• B. A $2\mathrm{kg}$ ball moving at $10m/s$
• C. A $10\mathrm{kg}$ box moving at $4m/s$
• D. A $5\mathrm{kg}$ cart moving at $6m/s$

Answer: (C)

Verified step by step guidance

1. Recall that momentum \(p\) is given by the product of mass \(m\) and velocity \(v\): \(p = m \times v\).
2. Calculate the initial momentum for each object by multiplying its mass and velocity: \(p_{\text{object}} = m_{\text{object}} \times v_{\text{object}}\).
3. Since the objects need to be stopped, the change in momentum \(\Delta p\) is equal to the initial momentum (because the final momentum is zero): \(\Delta p = p_{\text{initial}} - 0 = p_{\text{initial}}\).
4. Compare the values of \(\Delta p\) for all objects to determine which one requires the greatest change in momentum to stop.
5. Identify the object with the largest \(\Delta p\) as the one that requires the greatest change in momentum to stop its motion.