Crossing Trains and Extended Bodies
For collinear bodies of lengths L1 and L2, complete crossing time is (L1+L2)/|v1-v2| with signed velocities. Passing a point or pole uses only the moving body's length.
Why this shows up in the exam
Train-crossing questions · Vehicles passing platforms · Same-direction versus opposite-direction timing
Learn the idea
Complete crossing time equals the total length to clear divided by the relative speed. For two trains to pass completely, their full combined lengths must slide past one another. The relevant sliding rate is the relative speed, not either train's ground speed alone.
🧠 Memory hook: Length to clear over relative speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- t_cross = (L1+L2)/|v1-v2| — complete crossing of two extended bodies
- t_pole = L/|v| — time for one body to pass a fixed point
How to approach it
- 1Draw the first-contact and last-contact states
- 2Compute required clearance length
- 3Divide by the magnitude of signed relative velocity
Common slip-ups that cost marks
- •Using one train length for two-train crossing
- •Adding same-direction speeds
- •Forgetting to convert km/h to m/s
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A particle has initial speed 2 m/s and constant acceleration 3 m/s^2 for 4 s. What distance does it cover?
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