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NEET 2023 Physics Question 12 Solution

Topic: Motion in a Straight Line · Official NTA Booklet Code G5

Question

A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is:

✓

Verified Against NTA Final Answer Key

Option (4) : 4ϑ / 3

📚 Motion in a Straight Line Easy

📋 Given Parameters & Problem Setup

First Segment Distance Half the total distance (d)

First Segment Speed ϑ

Second Segment Distance Remaining half distance (d)

Second Segment Speed 2ϑ

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The 30-Second Exam Hall Shortcut: ⚡ Harmonic Mean Formula for Equal Distance Halves

⏱️ Save ~40 seconds

For equal distance halves, average speed is the harmonic mean: v_avg = 2 v₁ v₂ / (v₁ + v₂) = 2(ϑ)(2ϑ) / (3ϑ) = 4ϑ/3 in 10 seconds!

1 Recognize that the distance segments are equal (d₁ = d₂ = d).

2 Use the standard harmonic mean shortcut: v_avg = 2 v₁ v₂ / (v₁ + v₂).

3 Substitute v₁ = ϑ and v₂ = 2ϑ: v_avg = 2(ϑ)(2ϑ) / (ϑ + 2ϑ) = 4ϑ² / (3ϑ) = 4ϑ / 3.

4 Avoid the arithmetic mean trap (3ϑ/2 = 1.5ϑ); harmonic mean is always less than arithmetic mean!

5 Immediately pick Option (4)!

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Why You Can 100% Trust This Shortcut: Fundamental Kinematics · Rectilinear Motion (Harmonic mean of speeds for equal distance intervals: v_avg = 2 v₁ v₂ / (v₁ + v₂)).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Definition of Average Speed

Average speed is fundamentally defined as total distance travelled divided by total time elapsed:

v_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}}

Step 2

Time Calculation for Each Distance Half

Let the total distance be 2d. Each half of the journey has distance d:

t_1 = \frac{d}{\vartheta}, \qquad t_2 = \frac{d}{2\vartheta}

Step 3

Total Time Calculation

Add the two time intervals together using a common denominator:

t_{\text{total}} = t_1 + t_2 = \frac{d}{\vartheta} + \frac{d}{2\vartheta} = \frac{2d + d}{2\vartheta} = \frac{3d}{2\vartheta}

Step 4

Evaluation of Average Speed

Divide total distance 2d by total time:

v_{\text{avg}} = \frac{2d}{\frac{3d}{2\vartheta}} = 2d \times \frac{2\vartheta}{3d} = \frac{4\vartheta}{3}

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360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Inverted reciprocal of 4/3.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate inverted the numerator and denominator, calculating Total Time / Total Distance.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Severe underestimation, smaller than both individual speeds.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate subtracted speeds or miscalculated intermediate fractions.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Missing factor of 2 in total distance numerator.

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Student Fallacy (Why candidates pick this trap): Candidate forgot that total distance is 2d (d + d) and used d in the numerator (d / (3d/2ϑ) = 2ϑ/3).

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate harmonic mean average speed for two equal distance segments.

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Why this is airtight: None. Candidate correctly applied total distance over total time.

⚠️

NTA Trap Alert: Arithmetic Mean Trap vs Harmonic Mean (Picking 3ϑ/2)

Students frequently make the fatal mistake of simply averaging the two speeds: (ϑ + 2ϑ)/2 = 1.5ϑ. Arithmetic mean is ONLY valid for equal TIME intervals, never for equal DISTANCE intervals.

🛡️ How to avoid the -1 mark: Remember: Equal distance = Harmonic mean (2v₁v₂ / (v₁+v₂)). Equal time = Arithmetic mean ((v₁+v₂)/2).

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Motion in a Straight Line Standard Benchmark

Core Scientific Principle Tested:

"Average speed is total path length divided by total elapsed time. For equal distance intervals, v_avg is the harmonic mean of the speeds."

Syllabus Focus: Average Speed and Rectilinear Kinematics

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 12 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Harmonic Mean Formula for Equal Distance Halves

Step-by-Step Rigorous Workflow & Mathematical Proof

Definition of Average Speed

Time Calculation for Each Distance Half

Total Time Calculation

Evaluation of Average Speed

360° Option Elimination Engine Key Feature

NTA Trap Alert: Arithmetic Mean Trap vs Harmonic Mean (Picking 3ϑ/2)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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