Guide to Game Development/Theory/Physical motion/SUVATs

Basics

SUVAT is a collection of all of the letters used for variables in basic motion equations. Template:Dbox Template:Dbox Template:Dbox Template:Dbox Template:Dbox

The equations you'll need

These are the equations you need to know:

$\bar{v}=\frac{\mathrm{\Delta }s}{\mathrm{\Delta }t}$

$\bar{a}=\frac{\mathrm{\Delta }v}{\mathrm{\Delta }t}$

$v=u+at$

$s=ut+\frac{a{t}^2}{2}$

Velocity time graph where the acceleration is represented as the gradient by a green line.

$s=vt-\frac{a{t}^2}{2}$

$v^2=u^2+2as$

$s=\frac{u+v}{2}t$

If you were to plot a distance time graph, the gradient would be velocity. If the graph is curved, it shows that there is a change in velocity and the object is accelerating

If you were to plot a velocity time graph, then the area under the graph will represent the displacement, while the gradient of the line represents acceleration. A straight line represents constant acceleration whilst a curved line shows acceleration is changing

If you were to plot an acceleration time graph, then the area under the curve will represent the velocity.

Template:CPTAnswerTab $u=0,s=1000m,t=40sec,a=?,v=?$

1. Finding $a$:

using: $s=ut+\frac{a{t}^2}{2}$

$1000=0*40+\frac{1}{2}a*40^2$

$1000=800a$

$a=\frac{1000}{800}=1.25m{s}^{-2}$

2. Finding $v$:

using: $v=u+at$

$v=0+1.25*40$

$v=50m{s}^{-1}$

Vector quantities

Template:Main What's a vector? In one sentence, a vector is a quantity with a magnitude and a direction. Template:Dbox Template:Dbox

Note, that if you want to find either the displacement, speed or acceleration as a number, then you'll need to find the magnitude of the vector, follow these respectfully: $|s|,|v|,|a|$