Uniform Acceleration Motion: Equations with Explanations

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:


definition of acceleration: a = (v - u) / t


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 x0 = 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 x0 = 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