In basic kinematics, the rate of change of displacement of a body with respect to time is known by which standard term?

Introduction / Context:
In the study of motion, or kinematics, several related quantities describe how the position of an object changes with time. These include displacement, velocity, speed, and acceleration. This question specifically targets the definition of velocity in terms of displacement and time. Understanding these basic definitions is crucial before tackling more complex motion problems in one or more dimensions.

Given Data / Assumptions:
- A body undergoes displacement as time passes.- The quantity of interest is the rate at which displacement changes with time.- We assume standard definitions used in introductory physics.

Concept / Approach:
Displacement is a vector quantity that describes the change in position of a body, including both magnitude and direction. Velocity is defined as the rate of change of displacement with respect to time and is therefore also a vector quantity. Mathematically, average velocity = change in displacement / time interval. Instantaneous velocity is defined through the derivative of displacement with respect to time in calculus. Speed, on the other hand, is the rate of change of distance (a scalar), and acceleration is the rate of change of velocity, not displacement.

Step-by-Step Solution:
1. Recall the definition of displacement as the shortest distance from the initial to the final position of the body in a specified direction.2. Recall that velocity is defined as displacement divided by time, making it the rate of change of displacement with time.3. Recognise that speed uses distance, not displacement, and is a scalar.4. Recognise that acceleration is defined as the rate of change of velocity with time, not displacement.5. Recognise that distance is itself a measure of length travelled and is not a rate of change quantity.6. Therefore, the correct term for rate of change of displacement is velocity.

Verification / Alternative check:
In standard formulas, velocity v is written as v = s / t, where s is displacement and t is time. Acceleration a is written as a = change in velocity / time. These two relations together verify that velocity is the first derivative of displacement with respect to time, while acceleration is the second derivative. Textbooks consistently state this hierarchy, which confirms that velocity is the rate of change of displacement.

Why Other Options Are Wrong:
- Acceleration: It measures how quickly velocity changes, not how displacement changes directly.- Speed: It is based on distance per unit time, has no direction, and therefore does not fully describe change in displacement.- Distance: It is a scalar measure of ground covered and is not defined as a rate of change.

Common Pitfalls:
Some learners confuse speed and velocity because both have the same dimensions of length per time. The key difference is that velocity uses displacement, includes direction, and fits the vector nature of motion. Remembering that acceleration is one step higher, relating to velocity change, will also help avoid mixing up these definitions in exam questions.

Final Answer:
The rate of change of displacement with time is called velocity.