Consider a car applying brakes. Which of the following quantities would have a negative value? 1. Distance travelled ($s$). 2. Acceleration ($a$). 3. Change in velocity ($v - u$). Select the correct answer using the code given below:

Correct Option The correct option is (c). Explanation In kinematics, physical quantities are categorized as scalars or vectors. Scalars possess only magnitude and are generally positive (e.g., distance), whereas vectors possess both magnitude and direction, allowing them to take negative values based on the direction of motion relative to a reference frame. When a vehicle brakes, it undergoes retardation. Statement-wise Analysis - Statement 1 is Incorrect: Distance ($s$) refers to the total length of the path covered by a moving body. It is a scalar quantity and is always positive, regardless of the direction of motion or the forces applied. - Statement 2 is Correct: Acceleration ($a$) is a vector quantity defined as the rate of change of velocity. When brakes are applied, the acceleration acts in the direction opposite to the velocity to reduce speed. In a standard coordinate system where forward motion is positive, this opposing acceleration (retardation) is negative. - Statement 3 is Correct: The change in velocity is calculated as Final Velocity ($v$) minus Initial Velocity ($u$). During braking, the speed decreases, meaning the final velocity is less than the initial velocity ($v < u$). Therefore, the difference ($v - u$) results in a negative value. Key Takeaway: Distance is a scalar quantity and cannot be negative. Acceleration and change in velocity are vector quantities; during retardation (braking), they are directed opposite to the motion and are mathematically negative.

Consider a car applying brakes. Which of… - NCERT Class 9 Science MCQ

NCERT Class 9 Science — Chapter 1: Motion

mcqmedium

Consider a car applying brakes. Which of the following quantities would have a negative value?

Distance travelled ($s$).
Acceleration ($a$).
Change in velocity ($v - u$).

Select the correct answer using the code given below:

NCERT textbook question

From NCERT Science - class 9 · Page 11

Options

A1 and 2 only
B2 only
C2 and 3 only
D1, 2 and 3

Did you get this right?

Solution

Correct Option

The correct option is (c).

Explanation

In kinematics, physical quantities are categorized as scalars or vectors. Scalars possess only magnitude and are generally positive (e.g., distance), whereas vectors possess both magnitude and direction, allowing them to take negative values based on the direction of motion relative to a reference frame. When a vehicle brakes, it undergoes retardation.

Statement-wise Analysis

Statement 1 is Incorrect: Distance ($s$) refers to the total length of the path covered by a moving body. It is a scalar quantity and is always positive, regardless of the direction of motion or the forces applied.
Statement 2 is Correct: Acceleration ($a$) is a vector quantity defined as the rate of change of velocity. When brakes are applied, the acceleration acts in the direction opposite to the velocity to reduce speed. In a standard coordinate system where forward motion is positive, this opposing acceleration (retardation) is negative.
Statement 3 is Correct: The change in velocity is calculated as Final Velocity ($v$) minus Initial Velocity ($u$). During braking, the speed decreases, meaning the final velocity is less than the initial velocity ($v < u$). Therefore, the difference ($v - u$) results in a negative value.

Key Takeaway: Distance is a scalar quantity and cannot be negative. Acceleration and change in velocity are vector quantities; during retardation (braking), they are directed opposite to the motion and are mathematically negative.

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