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.