In introductory mechanics, how is an object's linear momentum related to its mass and velocity?

• A. Momentum is proportional to mass: $p=mv$.
• B. Momentum is inversely proportional to mass: $p=\frac{v}{m}$.
• C. Momentum is independent of mass: $p=v$.
• D. Momentum is proportional to the square of mass: $p=m^{2}v$.

Answer: (A)

Verified step by step guidance

1. Recall the definition of linear momentum in classical mechanics, which describes the quantity of motion an object has.
2. Understand that linear momentum \(p\) depends on two key properties of the object: its mass \(m\) and its velocity \(v\).
3. Express the relationship mathematically as \(p = m \times v\), meaning momentum is directly proportional to both mass and velocity.
4. Recognize that this formula implies if either mass or velocity increases, the momentum increases proportionally.
5. Note that momentum is not inversely proportional to mass, nor independent of mass, nor proportional to the square of mass; the correct and standard formula is \(p = m v\).