Question

If a moving body changes its position from \(x_1\) to \(x_2\) in a time interval \(\Delta t\), then \(\frac{x_2 - x_1}{\Delta t}\) is defined as

• A. average acceleration
• B. average velocity
• C. instantaneous acceleration
• D. instantaneous velocity
• E. average displacement

Hint:

Velocity is displacement/time, while speed is distance/time.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question asks for the definition of a fundamental kinematic quantity. We need to analyze the given expression and relate it to the standard definitions of motion.
Step 2: Detailed Explanation:
Let's break down the expression \( \frac{X_2 - X_1}{\Delta t} \):
Numerator (X\(_2\) - X\(_1\)): This term represents the change in position of the body. The change in position is also known as displacement (\(\Delta\)X).
Denominator (\(\Delta\)t): This term represents the time interval over which the change in position occurred.
The expression is therefore the total displacement divided by the total time interval.
By definition:
Average velocity (\(\bar{v}\)) is defined as the total displacement divided by the total time interval. \[ \bar{v} = \frac{\text{Total Displacement}}{\text{Total Time Interval}} = \frac{\Delta X}{\Delta t} = \frac{X_2 - X_1}{\Delta t} \]
Average acceleration (\(\bar{a}\)) is the change in velocity (\(\Delta\)v) divided by the time interval (\(\Delta\)t).
Instantaneous velocity (v) is the limit of the average velocity as the time interval approaches zero, i.e., the derivative of position with respect to time (\(v = dX/dt\)).
Instantaneous acceleration (a) is the limit of the average acceleration as the time interval approaches zero (\(a = dv/dt\)).
Average displacement is not a standard term; displacement itself is the change in position.
The given expression exactly matches the definition of average velocity.
Step 3: Final Answer:
The expression \( \frac{X_2 - X_1}{\Delta t} \) is defined as average velocity. This corresponds to option (B).