Which one of the following physical quantities is not a vector quantity and therefore has magnitude only but no direction associated with it?

Introduction / Context:

In mechanics, physical quantities are classified as scalars or vectors. Scalars have magnitude only, while vectors have both magnitude and direction and obey the rules of vector addition. This classification is fundamental for correctly applying Newton laws and kinematics. The question asks you to select the quantity that is not a vector from the given list.

Given Data / Assumptions:

• Momentum is considered as mass times velocity.
• Displacement is the change in position from initial to final point.
• Torque is associated with rotational effect of a force about a point or axis.
• Speed is the rate of change of distance with time.

Concept / Approach:

A vector quantity has both magnitude and direction and transforms according to vector laws. Displacement has a specific direction from the initial to the final position, so it is a vector. Momentum is mass times velocity; since velocity is a vector, momentum is also a vector. Torque is defined as the cross product of position vector and force, and hence is a vector (more precisely a pseudovector). Speed, however, is defined as the magnitude of velocity without any directional information; it is a scalar quantity. Therefore, among the options, speed is the only non vector quantity.

Step-by-Step Solution:

Verification / Alternative check:

Consider algebraic operations. Vectors must be added using head to tail or component wise rules. You cannot meaningfully add two speeds with directions to get a resultant speed vector; instead you would add velocities if direction matters. In contrast, displacement, momentum and torque can be broken into components along axes and added as vectors, which further confirms their vector nature.

Why Other Options Are Wrong:

Option A: Momentum has direction opposite to applied force during deceleration and along the direction of motion when moving, demonstrating vector character.

Option B: Displacement, unlike distance, depends on direction from start to end point and can cancel when a path returns to the origin.

Option C: Torque produces rotation about an axis and changes when the force direction changes, exhibiting vector behaviour.

Common Pitfalls:

Students occasionally confuse speed with velocity. Velocity is a vector because it includes direction; speed is the magnitude of velocity only. Remember that every vector has a corresponding scalar magnitude, and confusing the two can lead to errors in conceptual questions. Carefully read whether the question refers to speed or velocity.

Final Answer:

The quantity that is not a vector is Speed.