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
v = at 
1

x = (1/2) a t^{ 2}

2 
x = (1/2) v t 
3 
v^{2} = 2 a x

4 
