Position to acceleration
This page provides some examples of how acceleration is calculated if the position formula is known.
Physics equations
x(t) = position
v(t) = velocity (speed)
a(t) = acceleration

v(t) = x'(t)
a(t) = v'(t) = x''(t)

Example 1
x(t) = 5
v(t) = 0
a(t) = 0
When the position is a constant, the velocity will be zero as well as the acceleration.
Example 2
x(t) = 8t
v(t) = 8
a(t) = 0
When the position is a first order function, the velocity will be constant and the accerelation is zero.
Example 3
x(t) = 3t2
v(t) = 6t
a(t) = 6
In this case, the position is a second order function. This means that the velocity is a first order function and the acceleration is constant. This is called an uniformly accelerated motion.
Example 4
x(t) = t3
v(t) = 3t2
a(t) = 6t
When the position is a third order function, the velocity is a second order function and the acceleration will be a first order function.