NCERT Class 9 Science — Chapter 1: Motion

mcqeasy

In kinematics, 'acceleration' is defined as:

Official previous-year question

Verified 1 Aug 2026.

Options

AThe product of velocity and time.
BThe ratio of total distance to total time.
CThe rate of change of position with time.
DThe rate of change of velocity with time.

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Solution

The correct option is

The rate of change of velocity with time.

Explanation

In kinematics, the study of motion without considering its causes, physical quantities are defined to describe the movement of objects. Acceleration is a derived vector quantity that measures the variation in velocity over a specific duration.

Analysis of Options:

The rate of change of position with time. is incorrect: The rate of change of position with respect to time is defined as velocity. It indicates the speed and direction of an object's displacement.
The rate of change of velocity with time. is correct: Acceleration is defined as the rate of change of velocity with time. It quantifies how quickly an object speeds up, slows down, or changes its direction. Mathematically, instantaneous acceleration is expressed as a = dv/dt.
The product of velocity and time. is incorrect: The product of velocity and time represents displacement (assuming uniform velocity). It indicates the change in position rather than the rate of change of motion.
The ratio of total distance to total time. is incorrect: The ratio of total distance traveled to the total time taken is defined as average speed. Unlike acceleration, speed is a scalar quantity and does not account for direction.

Key Takeaway:

Acceleration is strictly the time rate of change of velocity. An object accelerates whenever its speed changes, its direction changes, or both change simultaneously.

Your note

More from Chapter 1: Motion

With reference to non-uniform acceleration, consider the following statements: 1. It occurs when velocity changes by unequal amounts in equal intervals of time. 2. A car increasing its speed by equal amounts in equal intervals of time is an example of non-uniform acceleration. 3. Free fall of a body is an example of non-uniform acceleration. Which of the statements given above is/are correct?

medium

Consider the following statements regarding the speed of sound and light: 1. Light travels faster than sound. 2. Thunder is heard before lightning is seen. 3. The speed of sound in air is approximately 346 km/s. Which of the statements given above is/are correct?

easy

In a hammer throw event, the hammer moves along a straight line tangential to the circular path upon release. This is because:

medium

With reference to the description of motion, consider the following statements: 1. The position of an object is described by specifying a reference point known as the origin. 2. An object's state of motion is absolute and independent of the observer. 3. Motion is inferred through the change in position of an object over time. Which of the statements given above are correct?

medium

Consider the following statements regarding 'distance' and 'displacement': 1. Distance is a vector quantity requiring both magnitude and direction. 2. Displacement is the shortest distance measured from the initial to the final position of an object. 3. The magnitude of displacement is equal to distance when motion is in a straight line. Which of the statements given above is/are correct?

easy

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The correct option is

The rate of change of velocity with time.

Explanation

Analysis of Options:

The rate of change of position with time. is incorrect: The rate of change of position with respect to time is defined as velocity. It indicates the speed and direction of an object's displacement.
The rate of change of velocity with time. is correct: Acceleration is defined as the rate of change of velocity with time. It quantifies how quickly an object speeds up, slows down, or changes its direction. Mathematically, instantaneous acceleration is expressed as a = dv/dt.
The product of velocity and time. is incorrect: The product of velocity and time represents displacement (assuming uniform velocity). It indicates the change in position rather than the rate of change of motion.
The ratio of total distance to total time. is incorrect: The ratio of total distance traveled to the total time taken is defined as average speed. Unlike acceleration, speed is a scalar quantity and does not account for direction.

Key Takeaway:

Acceleration is strictly the time rate of change of velocity. An object accelerates whenever its speed changes, its direction changes, or both change simultaneously.