General SciencePhysics: Work, Energy and Power

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The kinetic energy of a body is defined by the formula $KE = 0.5 mv^2$ . Which of the following factors does it depend on? i) Mass of the object, ii) Square of the velocity, iii) Acceleration due to gravity.

Only i

Only ii

i and ii

i, ii and iii

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Work, Energy and Power

Option C

i and ii

Quick Summary:

Kinetic energy is the energy possessed by an object due to its motion. According to the formula $KE = 0.5 mv^2$ , it depends explicitly on the mass ( $m$ ) of the object and the square of its velocity ( $v^2$ ).

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of a car on a highway: a heavier truck (more mass) hits harder than a light bike at the same speed, and increasing speed makes the impact much more severe because energy increases with the square of the velocity.

🧠 Memory Mnemonic / Shortcut Aid

MVS: Mass, Velocity-squared, Scalar (energy is a scalar quantity).

🔢 Key Formulas

$KE = \frac{1}{2}mv^2$ — Kinetic Energy definition

$v^2 = u^2 + 2as$ — Kinematic relation relating velocity to acceleration

⚙️ Working Principle

The Work-Energy Theorem states that the work done on an object equals its change in kinetic energy. Since the formula involves scalar quantities (mass and speed), the orientation or the presence of an external field like gravity does not define kinetic energy itself, although gravity can change velocity over time.

📌 Key Points

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Kinetic energy is a scalar quantity.
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Doubling the velocity increases the kinetic energy by a factor of four.
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Acceleration due to gravity affects potential energy ( $PE = mgh$ ), not the definition of kinetic energy.
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The SI unit of kinetic energy is the Joule ( $J$ ).

✅ Advantages

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Allows calculation of energy based on observable motion properties.

❌ Disadvantages / Limitations

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Does not account for relativistic speeds where $KE = (\gamma - 1)mc^2$ applies.

🛠️ Applications / Uses

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Determining braking distances for vehicles.
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Designing safety features like crumple zones in automobiles.

📄 Additional Information

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Kinetic energy is always non-negative because mass is positive and $v^2$ is always positive or zero.
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Option iii is incorrect because acceleration due to gravity is a property of the environment/field, not an intrinsic variable in the formula for kinetic energy.

📊 Diagram / Illustration

✅

C is correct — Kinetic energy is mathematically dependent only on the mass of the object and the square of its velocity.

Core Concepts Used

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Kinetic Energy Scalar Quantities Classical Mechanics

💡 EXAM TIP

Always distinguish between Kinetic Energy ( $KE = \frac{1}{2}mv^2$ ) and Potential Energy ( $PE = mgh$ ). Gravity is vital for $PE$ , while velocity is the driver for $KE$ .

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