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 t_{1}
v be the final velocity at time t_{2}
t = t_{ 2} - t_{1}
x is the displacement between t_{1} and t_{2}
x_{0} 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 + x_{0}

2

x = (1/2)(u + v) t + x_{0}

3

v^{ 2} = u^{ 2} + 2 a (x - x_{0})

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