Piecewise and Multi-Stage Motion
For piecewise kinematics, x and v remain continuous across a boundary without an impulsive event, while acceleration may jump. Total elapsed time, displacement, and distance are assembled from the stage intervals with their signs.
Why this shows up in the exam
Accelerate-coast-brake journeys · Parachute opening · Motion with multiple graph segments
Learn the idea
At each stage boundary, carry forward position and velocity unless the source states an impulse or discontinuity. Real motion often changes rules: accelerate, coast, brake, or deploy a parachute. Solve one stage at a time, using the ending state of one stage as the starting state of the next.
🧠 Memory hook: End one stage, hand its x and v to the next.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- xᵢ₊₁(0) = x_i(t_i) — position continuity at a stage boundary
- vᵢ₊₁(0) = v_i(t_i) — velocity continuity when no impulse acts
- Delta x_total = sum(Delta x_i) — signed displacement accumulated across stages
How to approach it
- 1Draw a stage timeline
- 2Solve each interval with local data
- 3Transfer boundary values and combine only the requested totals
Common slip-ups that cost marks
- •Restarting velocity at every stage
- •Using one acceleration for the whole trip
- •Adding signed displacements when total distance is asked
🌟 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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