Kinematics terminology — precise definition: The rate of change of displacement of a body with respect to its surroundings is known as which of the following quantities?

Introduction / Context:
Clear terminology in kinematics avoids design and analysis mistakes. Displacement, velocity, speed, and acceleration each have specific meanings used in motion studies for mechanisms, vehicles, and structures subjected to dynamic loads.

Given Data / Assumptions:

• Displacement is a vector (magnitude and direction).
• Time is continuous; differentiability assumed.
• Reference to “with respect to its surroundings” indicates measurement in a chosen inertial frame.

Concept / Approach:

Velocity is defined as the time rate of change of displacement: v = ds/dt (vector quantity). Speed is the magnitude of velocity and equals the time rate of change of distance traveled, which is scalar. Acceleration is the rate of change of velocity: a = dv/dt. Jerk is the rate of change of acceleration: j = da/dt.

Step-by-Step Solution:

Verification / Alternative check:

In component form, if displacement s(t) has components x(t), y(t), z(t), then velocity vector v(t) = (dx/dt, dy/dt, dz/dt). This matches the definition requested.

Why Other Options Are Wrong:

Acceleration (b) differentiates velocity, not displacement directly; speed (c) discards direction; “none of these” (d) is false; jerk (e) is a higher derivative not asked for.

Common Pitfalls:

Interchanging speed and velocity; ignoring vector nature leading to sign/direction errors in analyses.

Final Answer:

velocity