In introductory mechanics, what is the relationship between an object's momentum and its velocity (for constant mass)?

• A. $p=m{v}^2$, so momentum is proportional to the square of velocity
• B. $p=mv$, so momentum is directly proportional to velocity
• C. $p=\frac{v}{m}$, so momentum is inversely proportional to mass
• D. $p=m+v$, so momentum equals mass plus velocity

Answer: (B)

Verified step by step guidance

1. Recall the definition of momentum in classical mechanics: momentum \(p\) is the product of an object's mass \(m\) and its velocity \(v\).
2. Express this relationship mathematically as \(p = m \times v\).
3. Understand that if the mass \(m\) is constant, momentum \(p\) changes directly with velocity \(v\), meaning they are proportional to each other.
4. Note that momentum is not proportional to the square of velocity, nor is it the sum or ratio of velocity and mass; these forms do not correctly represent momentum.
5. Therefore, the correct relationship is that momentum equals mass times velocity, showing a direct proportionality between momentum and velocity for constant mass.