In introductory physics, which statement best defines the linear momentum of an object?

• A. Momentum is a vector equal to mass times velocity: $p=mv$.
• B. Momentum is the rate of change of position with time: $p=\frac{dx}{dt}$.
• C. Momentum is the product of force and time: $p=Ft$.
• D. Momentum is a scalar equal to mass times speed: $p=mv$, where $v$ is speed only.

Answer: (A)

Verified step by step guidance

1. Understand that linear momentum is a physical quantity that describes the motion of an object and depends on both its mass and velocity.
2. Recall the definition of velocity as a vector quantity, which means it has both magnitude and direction, unlike speed which is only magnitude.
3. Recognize that linear momentum \( \mathbf{p} \) is defined as the product of an object's mass \( m \) and its velocity \( \mathbf{v} \), expressed mathematically as \( \mathbf{p} = m \mathbf{v} \).
4. Note that momentum is a vector quantity because it depends on velocity, which includes direction, so momentum also has direction.
5. Distinguish this from other options: momentum is not the rate of change of position (which is velocity), nor is it simply force times time (which relates to impulse), and it is not a scalar quantity.