The Question is from NEET guide , and it was created by the author NAGA SAI

Question

If the speed of an object is doubled, its kinetic energy will:

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [Option B]
## CONCEPT FRAMEWORK
	**Primary Concept**: Kinetic Energy
	**Related Topics**: Work-Energy Theorem, Motion
	**Prerequisites**: Understanding of kinetic energy formula and its relation to velocity.
## SOLUTION PATHWAY
**Given Information**:
	Initial velocity = v
	Final velocity = 2v
	Kinetic energy formula: $KE = \frac{1}{2}mv^2$
**Method & Steps**:
	1. Define the initial kinetic energy (KE1).
		Reasoning:  We need to express the initial kinetic energy using the given formula.
		Formula/Rule: $KE_1 = \frac{1}{2}mv^2$
	2. Define the final kinetic energy (KE2) when speed is doubled.
		Working: Substitute 2v for v in the kinetic energy formula.
		Key Point:  Remember to square the entire 2v term.
		Formula/Rule: $KE_2 = \frac{1}{2}m(2v)^2 = \frac{1}{2}m(4v^2) = 4(\frac{1}{2}mv^2)$
	3. Compare the final and initial kinetic energies.
		Result: $KE_2 = 4KE_1$. Therefore, the kinetic energy increases by a factor of 4.
		Verification: This matches with the calculated increase factor.
## OPTION ANALYSIS
[A] :x: [Doubling the speed quadruples the kinetic energy, not doubles it.]
[B] ✓: [Since $KE_2 = 4KE_1$, the kinetic energy increases by a factor of 4.]
[C] :x: [Halving the kinetic energy would occur if the speed was reduced, not increased.]
[D] :x: [The kinetic energy is directly affected by changes in speed.]
## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Forgetting to square the velocity term in the kinetic energy formula, leading to incorrect calculations. [How to avoid]: Always remember the velocity term is squared in the formula.
		2.[Error 2]:  Assuming a linear relationship between velocity and kinetic energy. [How to avoid]: Understand that kinetic energy is proportional to the square of the velocity.
	**Quick Tips**:
		1.[Helpful shortcut]: Remember that if the speed is multiplied by 'n', the kinetic energy is multiplied by 'n²'.
		2.[Memory aid]:  Think of KE as being related to 'velocity squared', not just velocity.

NAGA SAI · Answer

Double

NAGA SAI · Answer

The correct Option is "Increase by a factor of 4"

NAGA SAI · Answer

Halve

NAGA SAI · Answer

Remain the same

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