🥋 The Move
Pick a consistent sign and use the constant-acceleration set:
\[
v=u+at,\quad s=ut+\tfrac12 at^2,\quad v^2=u^2+2as,\quad s=\tfrac12(u+v)t.
\]
Solve for the unknowns without mixing frames or axes.
📘 Canonical Problem
A particle starts with speed \(u\) and moves with constant acceleration \(a\) for time \(t\). Find the displacement \(s\) and final speed \(v\).
- Given: \(u,\ a,\ t\)
- Find: \(s,\ v\)
- Assume: straight-line motion; \(a\) constant.
Sketch notes: Choose + direction. At \(t=0\): \(x=0\). Use one time-based and one time-free SUVAT as needed.
🔎 Setup
- \(v=u+at\).
- \(s=ut+\tfrac12 at^2\).
🧭 Full Breakdown (White-Belt Pace)
- Integrate \(a=\mathrm dv/\mathrm dt\) → \(v=u+at\).
- Integrate \(v=\mathrm ds/\mathrm dt\) with \(v=u+at\) → \(s=ut+\tfrac12 at^2\).
- Eliminate \(t\): \(v^2=u^2+2as\).
⚡ Exam-Speed Variant (Black Belt)
- Pick two equations that contain only your unknowns.
- Time-free target? Use \(v^2=u^2+2as\).
🧯 Common Traps
- Sign chaos. Fix + direction first; keep \(a\) signed.
- Using SUVAT with non-constant \(a\). Don’t.
- Average speed misuse. \( \bar v=(u+v)/2 \) only if \(a\) constant.
🎯 Quick Checks
- Units: \(s\,[\text{m}],\ v,u\,[\text{m/s}],\ a\,[\text{m/s}^2]\).
- Limits: \(a\!\to\!0\Rightarrow s\!\to\!ut\), \(v\!\to\!u\).
🧪 Practice Variant
Braking: car at \(v_0\) stops with constant \(a=-a_b\). Find stopping distance. → \(\boxed{s=\dfrac{v_0^2}{2a_b}}\).