A.1.6—Uniform acceleration equations

Uniform-acceleration model

SUVAT equations apply when acceleration is constant along the chosen one-dimensional axis:

$$v=u+at,\quad s=ut+\frac12at^2,\quad v^2=u^2+2as,\quad s=\frac{u+v}{2}t$$

Choose an equation

List the known and unknown quantities $s,u,v,a,t$. Select an equation containing the required unknown and only known quantities; keep signs consistent with the positive direction.

Check the model

A constant acceleration means equal changes in velocity in equal time intervals. Use separate horizontal and vertical equations only when the motion has been resolved into independent components.

Worked example from local Question Bank row 22687

A glider accelerates uniformly from rest to $27.0\,\mathrm{m\,s^{-1}}$ in $11.0\,\mathrm{s}$. Use $s=\frac{u+v}{2}t$:

$$s=\frac{0+27.0}{2}\times 11.0=148.5\,\mathrm{m}\approx149\,\mathrm{m}$$

The result is the launch-run displacement; the constant-acceleration assumption is essential.

Common trap

Do not use SUVAT when acceleration varies significantly with time or position. A formula can produce a neat number while still violating the model’s constant-acceleration assumption.