Acceleration-Time Graphs
The velocity change over an interval is Delta v = integral(a dt). Velocity follows from v(t) = v0 + integral_0^t a(tau)d tau, and position then requires a second integration.
Why this shows up in the exam
Time-varying acceleration · Maximum-velocity calculations · Building velocity graphs from acceleration data
Learn the idea
Area under an acceleration-time graph changes velocity, while its shape shows how acceleration varies. Acceleration adds or removes velocity moment by moment. A large positive area builds positive velocity; a negative area reduces it, but neither alone gives displacement without first reconstructing velocity.
🧠 Memory hook: On a-t, area changes v; integrate again for x.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta v = integral(a dt) — signed area under an acceleration-time curve
- v(t) = v0 + integral₀^t a(tau)d tau — velocity reconstructed from acceleration history
How to approach it
- 1Compute signed area to the requested time
- 2Add initial velocity
- 3Integrate or average velocity only if position is needed
Common slip-ups that cost marks
- •Calling acceleration area displacement
- •Forgetting initial velocity
- •Assuming zero acceleration means zero velocity
🌟 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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