Douglas Quadling A level Mechanics 1 Misc Ex Q 6;
I recently worked on a challenging mechanics problem involving a car and a van accelerating at different times. While discussing the solution, I noticed that even advanced solvers (including AI tools) often make logical mistakes in mechanics problems. Let me explain how I identified and corrected these issues.
The Problem: Motion of a Car and a Van
A car and a van are stopped at traffic lights with a 1-meter initial gap. The car accelerates at 1.5 m/s² until it reaches 15 m/s and then continues at this speed. The van follows the same motion but starts moving only after the car increases the gap to 4 meters.
The goal was to find:
- A formula for the distance traveled by the car.
- The time interval between the car and the van starting.
- The final distance between them when both reach 15 m/s.
The Logical Mistakes I Found in AI-Based Solutions
When I first got a solution (generated by AI), it had the following missing logical steps:
1️⃣ Ignoring That the Car Moves at Constant Velocity for 2 Extra Seconds
- The solution only considered the first 10 seconds of acceleration but ignored that the car continued at 15 m/s for 2 more seconds.
- Correction: I ensured that the car’s total journey lasted 12 seconds, not just 10.
2️⃣ Miscalculating the Van’s Acceleration Duration
- The AI assumed the van only accelerated for 8 seconds instead of the correct 10 seconds.
- Correction: The van starts after a 2-second delay, but it still accelerates for 10 seconds, just like the car.
3️⃣ Forgetting to Add the Initial 1-Meter Gap
- The AI solution only considered the motion of the vehicles but forgot that they weren’t starting from the same position!
- Correction: The final separation should include the 1-meter initial gap, making the correct answer 31 meters, not just 30 meters.
Final Corrected Solution
✅ Distance Formula for the Car
For 0 ≤ t ≤ 10 seconds (during acceleration):
s=0.75t2s = 0.75 t^2s=0.75t2
For 10 ≤ t ≤ 12 seconds (constant velocity):
s=75+15(t−10)s = 75 + 15(t – 10)s=75+15(t−10)
✅ Time Interval Between the Car and Van Starting
2 seconds
✅ Final Distance Between Them When Both Reach 15 m/s
Final gap=105−75+1=31 meters\text{Final gap} = 105 – 75 + 1 = 31 \text{ meters}Final gap=105−75+1=31 meters
I Specialize in Solving Complex Mechanics Problems!
This problem highlights how logical errors can creep into mechanics solutions, even in advanced problem-solving.
✅ I have solved all Douglas Quadling A-Level Mechanics problems and have deep experience in identifying and correcting logical mistakes like these.
✅ I specialize in step-by-step mechanics solutions that ensure nothing is missing logically.
✅ If you’re a student preparing for A-Level Mechanics or struggling with complex kinematics, dynamics, or forces problems, I can help!
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