Velocity – scalar or vector? Classify the physical quantity “velocity” with respect to directionality and magnitude.

Introduction / Context:
Precise classification of kinematic quantities is fundamental to mechanics. Confusing speed and velocity leads to incorrect vector equations of motion, momentum, and work-energy analyses.

Given Data / Assumptions:

• Standard Newtonian mechanics without relativistic effects.
• Velocity is defined as the time rate of change of displacement vector.

Concept / Approach:
Velocity has both magnitude and direction. It is expressed as v = dx/dt for one dimension, or as a vector derivative of position r(t). Speed is the magnitude |v| and is scalar. Many laws (e.g., momentum p = m * v) require vectors; direction changes matter even at constant speed (uniform circular motion).

Step-by-Step Solution:

Verification / Alternative check:
Component form in 2D or 3D, v = (vx, vy, vz). Directional changes at constant |v| imply acceleration (centripetal), reinforcing the vector nature.

Why Other Options Are Wrong:

• Scalar: confuses speed with velocity.
• “Scalar as well as vector”: definitions are mutually exclusive.
• “None”: incorrect because the vector definition is standard.
• Pseudo-scalar: not applicable to velocity.

Common Pitfalls:
Interchanging speed and velocity in energy and momentum problems.

Final Answer:
A vector quantity