The equations of motion allow us to calculate the basic motion of objects.
We can write equations for the movement of an object, if it has a constant acceleration (a), over a distance (s) in a time (t), with initial velocity (u), and final velocity (v).
We have a simple equation that we know already:
a = (v-u)/t, or in other words: v = u + at
We can add to these a few more:
s = ut + ½at2
v2 = u2 + 2as
We can also modify these to get some extra equations, e.g:
s = vt - ½at2
s = ½(u+v)t
u2 = v2 - 2as
By these means we can calculate all 5 of the parameters if we know 3.
If a car accelerates from 10m/s to 20m/s in 5 secs, what is it's acceleration?
Answer: a = (v-u)/t = (20-10)/5 = 2metres/sec/sec.
How far does it travel in this time?
Answer: s = ½(u+v)t = ½(10+20)x5 = 15x5 = 75metres.
Or: s = ut + ½at2 = (10x5) + (½ x 2 x 25) = 50+25 = 75metres.
If we didn't know the final velocity (speed), how would we calculate it?
Answer: v = u + at = 10 + (2 x 5) = 10+10 = 20metres/sec.
Or: v2 = u2 + 2as = 100 + (2x2x75) = 400, so v = 20metres/sec.