Why is $p$ (momentum) considered a vector quantity in physics?

• A. Because $p$ is always positive and does not depend on direction.
• B. Because $p$ is calculated using only the mass of an object, which is a scalar.
• C. Because $p$ is defined as the product of $F$ (force) and $t$ (time), both of which are scalars.
• D. Because $p$ depends on both the magnitude and direction of an object's $v$ (velocity), making it a vector.

Answer: (D)

Verified step by step guidance

1. Recall the definition of momentum: it is given by the product of an object's mass and its velocity, expressed as \(\mathbf{p} = m \mathbf{v}\).
2. Understand that mass (\(m\)) is a scalar quantity, meaning it has only magnitude and no direction.
3. Recognize that velocity (\(\mathbf{v}\)) is a vector quantity, which means it has both magnitude (speed) and direction.
4. Since momentum is the product of a scalar (mass) and a vector (velocity), the resulting momentum \(\mathbf{p}\) must also be a vector, inheriting the direction from velocity.
5. Therefore, momentum depends on both how much mass an object has and the direction in which it is moving, making it a vector quantity in physics.