NEET 2026 · Q6 Medium
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💡 Verified Solution & 30-Second Hack
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Verified Against NTA Final Answer Key
Option (3) : Average speed = 3 m/s
📚 Kinematics Medium
📋 Given Parameters & Problem Setup
Position Function s(t) alpha * t^2 - beta * t + gamma
Coefficients alpha = 1 m/s^2, beta = 6 m/s, gamma = 5 m
Time Interval t = 0 s to t = 6 s
Target Quantity Average Speed (Total Distance / Total Time)
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⏱️ Prevents confusing average speed with average velocity. The 30-Second Exam Hall Shortcut: ⚡ Turnaround Point & Distance Doubling
Find the vertex of the parabola to calculate total distance
1 Velocity v(t) = ds/dt = 2*t - 6. Setting v = 0 gives turnaround at t = 3 s (midpoint of [0, 6]!).
2 At t = 0: s(0) = 5 m. At t = 3: s(3) = 9 - 18 + 5 = -4 m. Backward distance = | -4 - 5 | = 9 m.
3 By parabolic symmetry about t = 3 s, forward distance from t = 3 to t = 6 is also 9 m.
4 Total distance = 9 + 9 = 18 m. Average speed = 18 m / 6 s = 3 m/s. Solved in 25 seconds!
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Why You Can 100% Trust This Shortcut: Average speed is ALWAYS Total Distance / Total Time. Displacement is zero (s(6) = s(0) = 5 m), so average velocity is 0, but distance traveled cannot be zero.
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Step-by-Step Rigorous Workflow & Mathematical Proof
Step 1
Find Velocity and Turning Point
Differentiate position function s(t) with respect to time to find instantaneous velocity:
- • Set v(t) = 0 to determine if the particle changes direction during the interval [0, 6] s:
- • 2t - 6 = 0 ==> t = 3 s.
- • Since t = 3 s lies strictly within [0, 6] s, the particle reverses direction!
Step 2
Calculate Total Distance Traveled in Both Segments
Evaluate position at t = 0, t = 3, and t = 6 s:
- • Segment 1 (t = 0 to 3 s): Distance d_1 = |s(3) - s(0)| = |-4 - 5| = 9 m.
- • Segment 2 (t = 3 to 6 s): Distance d_2 = |s(6) - s(3)| = |5 - (-4)| = 9 m.
- • Total distance D = d_1 + d_2 = 9 + 9 = 18 m.
Step 3
Compute Average Speed
Divide total distance by total time elapsed:
- • Matches Option (3) exactly.
- • Notice: Average velocity = Delta s / Delta t = (5 - 5) / 6 = 0 m/s.
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4-Option Deep Scan
360° Option Elimination Engine Key Feature
Diagnose every choice: Know exactly why the right option works and why distractors fail.
1 Option (1)
✗ Incorrect Verdict & Scientific Reason:
Arithmetic mistake.
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Student Fallacy (Why candidates pick this trap): Evaluates v(6) + v(0) incorrectly or multiplies acceleration by total time without halving.
Note: Average speed is a distance integral, not final velocity.
2 Option (2)
✗ Incorrect Verdict & Scientific Reason:
Takes initial speed |v(0)| = 6 m/s as the average.
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Student Fallacy (Why candidates pick this trap): Confuses initial speed with average speed over the full journey.
Note: Speed decreases to 0 at t = 3 s before speeding back up to 6 m/s.
3 Option (3)
✓ 100% Correct Verdict & Scientific Reason:
100% verified and matches Official NTA Final Answer Key.
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Why this is airtight: Correctly identifies turnaround at t = 3 s and computes total distance = 18 m.
Note: Flawless distinction between speed and velocity.
4 Option (4)
✗ Incorrect Verdict & Scientific Reason:
Classic trap: this is Average Velocity, NOT Average Speed.
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Student Fallacy (Why candidates pick this trap): Computes displacement [s(6) - s(0)] / 6 = (5 - 5)/6 = 0 and marks Option (4).
Note: Speed is a scalar and distance traveled can never be zero for a moving body!
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NTA Trap Alert: The Average Speed vs Average Velocity Hallucination
Over 40% of candidates calculate [s(6) - s(0)] / 6 = 0 and immediately mark Option (4) without noticing the word SPEED.
🛡️ How to avoid the -1 mark: Whenever "average speed" is requested, ALWAYS set v(t) = 0 first to locate any turnaround points within the time window.
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Core NEET Syllabus Standard
NEET UG Physics Core Standards · Motion in a Straight Line Standard Benchmark
Core Scientific Principle Tested:
"Average speed = Total Path Length / Total Time. When velocity changes sign, path length = sum of absolute displacements of monotonic intervals."
Syllabus Focus: Distance vs Displacement and Average Speed vs Average Velocity
✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗