In elementary physics, which of the following physical quantities is classified as a vector quantity with both magnitude and direction?

Introduction / Context:
Many beginners in physics struggle to distinguish between scalar and vector quantities. Scalars have only magnitude, while vectors have both magnitude and direction. This question checks your understanding of which commonly used physical quantities are vectors. Recognising vector quantities is essential for correctly adding, subtracting and resolving them in problems involving forces, motion and fields.

Given Data / Assumptions:
- The options are momentum, pressure, energy and work.
- Standard school-level definitions of these quantities are assumed.
- We use the usual distinction: vectors have both magnitude and direction and obey vector addition rules, whereas scalars do not involve direction in their definition.

Concept / Approach:
Momentum is defined as mass * velocity. Because velocity is a vector, momentum is also a vector and points in the same direction as velocity. Pressure is defined as force per unit area, but in basic physics it is treated as a scalar quantity that has a magnitude acting equally in all directions at a point. Energy is a scalar measure of the capacity to do work and has no direction. Work is defined as force * displacement * cos(theta) and is also a scalar result of the dot product between force and displacement.

Step-by-Step Solution:
Step 1: Recall that a vector must have both magnitude and a specific direction in space. Step 2: Momentum p is given by p = m * v, where v is velocity. Since velocity is a vector, momentum has direction and is therefore a vector. Step 3: Pressure is defined as P = F / A, but at a point in a fluid it acts equally in all directions and is treated as a scalar in basic physics. Step 4: Energy is a scalar quantity representing the ability to perform work, and it has no associated direction. Step 5: Work is the scalar product of force and displacement and yields a single scalar value, positive or negative, but not a vector.

Verification / Alternative check:
In vector diagrams, you normally represent vectors such as displacement, velocity, acceleration, force and momentum with arrows. You never represent energy, work or pressure with direction arrows because their numerical values do not depend on direction. For example, a ball thrown to the east and a ball thrown to the west with the same speed have equal but oppositely directed momenta, confirming that momentum has direction and is a vector.

Why Other Options Are Wrong:
Pressure: Although it is related to force, in elementary physics pressure is treated as a scalar that has magnitude only and is the same in all directions at a point in a fluid.
Energy: Energy is a measure of the capacity to do work and is scalar. It can be added as ordinary numbers without considering direction.
Work: Work is the scalar result of a dot product and may be positive or negative, but it does not point in any spatial direction, so it is not a vector quantity.

Common Pitfalls:
Students sometimes assume that any quantity derived from force must be a vector, which is not correct. Others confuse the idea that pressure acts "in all directions" with being a vector, whereas that phrase simply means it has the same scalar value in every direction at a point. Carefully checking definitions and whether direction is an essential part of the quantity helps avoid these mistakes.

Final Answer:
The only quantity listed that is a vector is momentum.