#Motion

PHYSICS

A particle accelerates uniformly from rest to 20 m/s in 5 s . What is the distance covered?

Given: A particle accelerates uniformly from rest to 20 m/s in 5 s . What is the distance covered? These values define the system as per NCERT data. Formula: Find a = v - v_0/t = 20 - 0/5 = 4 m/s². This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Use x = v_0 t + 1/2 a t² = 0 · 5 + 1/2 · 4 · (5)² = 0 + 2 · 25 = 50 m . The distance covered is 50 m . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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PHYSICS

A cyclist accelerates from 6 m/s at 1.5 m/s² for 5 s, then decelerates at 2 m/s² until its speed is 8 m/s . What is the

Given: A cyclist accelerates from 6 m/s at 1.5 m/s² for 5 s, then decelerates at 2 m/s² until its speed is 8 m/s . What is the total distance covered? These values define the system as per NCERT data. Formula: Phase 1: v = 6 + 1.5 · 5 = 13.5 m/s, x_1 = 6 · 5 + 1/2 · 1.5 · (5)² = 30 + 18.75 = 48.75 m. This is standard NCERT relation. Substitution & Calculation: Phase 2: 8 = 13.5 - 2 t Rightarrow t = 2.75 s, x_2 = 13.5 · 2.75 - 1/2 · 2 · (2.75)² = 37.125 - 7.5625 = 29.5625 m . Total = 48.75 + 29.5625 = 78.3125 m approx 78.31 m . Result: The computed value matches expected outcome and confirms correct choice as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Relevant Physics topic covering fundamental principles,

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Laws of Motion and Energy Conservation

A 6kg block slides down a frictionless incline from 10m height. What is its speed at the bottom? (Take g\=10m/s2)

Potential energy mgh=6×10×10=600J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 600 J. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.

Ref: NCERT Class 11 Physics > Chapter 6: Work, Energy and Power > Topic: Laws of Motion and Energy Conservation

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SI Units and Dimensional Formulae

In motion with constant acceleration in a plane, how are the x- and y-components of the motion related?

For motion with constant acceleration in a plane, the x- and y-components are independent of each other. The motion can be treated as two separate one-dimensional motions along perpendicular directions, with each component governed by its own constant acceleration. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that They are independent is correct because its dimensions and unit match the physical quantity asked.

Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae

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