Position-Time Graphs
For a differentiable x-t curve, the tangent slope is v = dx/dt; a secant slope gives average velocity. A physically valid single-particle graph assigns only one position to each instant.
Why this shows up in the exam
Finding rest and reversal times · Comparing particles on one plot · Testing whether a proposed motion graph is physically possible
Learn the idea
The slope of a position-time graph is velocity, and its changing slope reveals acceleration. A position-time graph is a diary of location. A steep rising segment means fast positive motion, a flat segment means rest, and a falling segment means motion in the negative direction.
🧠 Memory hook: On x-t, slope speaks velocity.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v_inst = slope of tangent to x-t graph — instantaneous velocity at a time
- v_avg = Delta x/Delta t — secant slope between two graph points
How to approach it
- 1Check axes and units
- 2Read secant or tangent slope as requested
- 3Track slope sign to identify reversals
Common slip-ups that cost marks
- •Reading graph height as velocity
- •Allowing two positions at one time
- •Using total graph length as distance
🌟 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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