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:
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 |