EduNinja

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.

[ 3 ]

Determine g using the photograph.

Describe motion

Position locates the object, velocity is the rate of change of position, and acceleration is the rate of change of velocity. Distance and speed are scalar; displacement and velocity are directed quantities.

Use the right model

For uniform acceleration:

$v=u+at,\quad s=ut+ rac12at^2,\quad v^2=u^2+2as$

For projectiles without drag, solve horizontal and vertical components with a shared time. Do not use these equations when acceleration is non-uniform.

Check the boundary

Ask whether the quantity is average or instantaneous, whether the route or endpoints matter, whether acceleration is constant, and whether a neglected force such as drag changes the model.

A.1.6—Uniform acceleration equations

Apply SUVAT Equations to Uniform Acceleration

Retrieve the A.1 Kinematics Model

A.1.6 Exam Analysis