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.

The equations you'll need
These are the equations you need to know:

$$\overline{v} = \frac{\Delta s}{\Delta t}$$

$$\overline{a} = \frac{\Delta v}{\Delta t}$$

$$v = u + at$$

$$s = ut + \frac{at^2}{2}$$



$$s = vt - \frac{at^2}{2}$$

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

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

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.

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

1. Finding $$a$$:
 * using: $$s = ut + \frac{at^2}{2}$$
 * $$1000 = 0*40 + \frac{1}{2}a*40^2$$
 * $$1000 = 800a$$
 * $$a = \frac{1000}{800} = 1.25ms^{-2}$$

2. Finding $$v$$:
 * using: $$v = u + at$$
 * $$v = 0 + 1.25*40$$
 * $$v = 50ms^{-1}$$

Vector quantities
What's a vector? In one sentence, a vector is a quantity with a magnitude and a direction.

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: $$|s|, |v|, |a|$$