The equations that quantitatively describes uniform acceleration motion are explained.
Let
a be the acceleration
u be the initial velocity at time t1
v be the final velocity at time t2
t = t 2 - t1
x is the displacement between t1 and t2
x0 is the initial position
The relationship between all the above quantities are given by the following equations:
| v = a t + u | 1 (deduced from above definition) |
| x = (1/2) a t 2 + u t + x0 | 2 |
| x = (1/2)(u + v) t + x0 | 3 |
| v 2 = u 2 + 2 a (x - x0) | 4 |
If x 0 = 0 (start from origin) , the above equations simplifies to
| v = a t + u | 1 |
| x = (1/2) a t 2 + u t | 2 |
| x = (1/2)(u + v) t | 3 |
| v 2 = u 2 + 2 a x | 4 |
If x 0 = 0 (start from origin) and u =0 (starting from rest) the above equations simplifies further to
| v = at | 1 |
| x = (1/2) a t 2 | 2 |
| x = (1/2) v t | 3 |
| v2 = 2 a x | 4 |
