Kinematics — Identify vector quantities:\nWhich of the following physical quantities are vectors in elementary mechanics?

Introduction / Context:
Physics distinguishes scalar and vector quantities. Scalars have magnitude only, whereas vectors have both magnitude and direction and follow vector addition laws (e.g., triangle or parallelogram rule). Correctly classifying displacement, velocity, and acceleration is crucial for solving motion problems and applying kinematic equations consistently.

Given Data / Assumptions:

• Motion is along straight or curved paths in Newtonian mechanics.
• Terms refer to standard definitions: linear displacement, linear velocity, linear acceleration.
• We assume three-dimensional vectors unless a 1D restriction is explicitly stated.

Concept / Approach:
Ask whether the quantity requires direction for full specification and obeys vector algebra. Displacement is the vector difference between final and initial position; velocity is the time rate of change of displacement; acceleration is the time rate of change of velocity. Each inherently includes direction.

Step-by-Step Solution:
Displacement: position_final − position_initial, direction matters → vector.Velocity: v = ds/dt, derived from displacement → vector.Acceleration: a = dv/dt, derived from velocity → vector.Therefore, all three listed quantities are vectors.

Verification / Alternative check:
If you reverse the direction of motion, displacement, velocity, and acceleration change sign (or direction), which is a hallmark of vector behavior. Their magnitudes alone would be insufficient to describe motion fully.

Why Other Options Are Wrong:

• Linear displacement: True but incomplete to select alone.
• Linear velocity: True but incomplete to select alone.
• Linear acceleration: True but incomplete to select alone.

Common Pitfalls:

• Confusing displacement (vector) with distance (scalar).
• Assuming “linear” implies scalar; “linear” here refers to translational motion, not the absence of direction.

Final Answer:
all of these