How do I isolate equations of speed?

Question

example: a=v2-v1
---------
delta t

Answer 1

Isolate? Derive?

Velocity is defined by how much distance you cover in a time interval in a certain direction (v=d/t going ___)

So it is easy to see if v=d/t then d=vt

Acceleration is defined by the increase in velocity over a time intervel. An increase in velocity can be found by subtracting the original velocity by the new velocity. Mathematically: a=(vf-v0)/t

So these are just definitions put into mathematical terms, with them you can derive other equations. Like:

if a=(vf-v0)/t then
vf=at+v0

if you want to find how much distance traveled, then you integrate at+v0 with respect to time.

vf*t=1/2(at^2)+v0t+c --- vf = d/t, so (d/t)t=d; c=x0 because you will always be displaced by as much as you started out.

d=1/2(at^2)+v0t+x0
So, you start with definitions and work from there.