Fundamental kinematics What is the physical quantity defined as the rate of change of displacement of a body with respect to time?

Introduction / Context:
This question checks core kinematics vocabulary used in physics and engineering. Displacement, velocity, acceleration, and momentum are often confused, yet each has a precise definition critical for motion analysis, control, and design.

Given Data / Assumptions:

• A moving body has a displacement s(t) measured from a reference point.
• Time t is continuous and differentiable for ordinary motions considered in mechanics.
• Standard SI units are used: displacement in metres (m) and time in seconds (s).

Concept / Approach:
Velocity is defined as the rate of change of displacement with respect to time. In calculus terms, instantaneous velocity v is the first time derivative of displacement: v = ds/dt. Acceleration a is the rate of change of velocity: a = dv/dt = d^2s/dt^2. Momentum p is mass * velocity: p = m * v.

Step-by-Step Solution:

Verification / Alternative check:
Consider uniform motion with s = k * t. Then ds/dt = k is constant (velocity), while dv/dt = 0 (acceleration). This confirms that the first derivative corresponds to velocity and not acceleration.

Why Other Options Are Wrong:

• Acceleration: Rate of change of velocity, not displacement.
• Momentum: Mass multiplied by velocity; not a rate of change.
• None of these: Incorrect because “velocity” precisely matches the definition.
• Speed: Magnitude of velocity only; the question refers to the vector rate (velocity) associated with displacement.

Common Pitfalls:
Using “speed” for any rate of motion. Speed lacks direction, whereas velocity incorporates direction and directly derives from displacement, which is a vector from a reference.

Final Answer:
velocity