Meeting, Catch-Up, and Pursuit
For particles A and B in one dimension, encounter times solve x_A(t) = x_B(t) within the allowed time domain. Multiple valid roots represent multiple crossings; tangency can represent contact without passing.
Why this shows up in the exam
Cars and buses starting at different points · Graphical overtaking · Repeated crossings under variable acceleration
Learn the idea
Objects meet when their position functions are equal at the same physical time. Catch-up is not decided by speed alone; the faster object must erase an initial gap. Position equations keep both the gap and any different accelerations visible.
🧠 Memory hook: Same place, same time: equate positions.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- x_A(t) = x_B(t) — common-position condition for an encounter
- gap(t) = x_A(t)-x_B(t) — relative position whose zeros are crossings
How to approach it
- 1Use one origin and clock
- 2Write both position functions
- 3Solve for all admissible roots and inspect repeated contact
Common slip-ups that cost marks
- •Equating velocities instead of positions
- •Ignoring the initial separation
- •Keeping negative or out-of-domain roots
🌟 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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