Position to acceleration

This page provides some examples of how acceleration is calculated if the position formula is known.

v(t) = velocity (speed)

a(t) = acceleration

v(t) = 0

a(t) = 0

When the position is a constant, the velocity will be zero as well as the acceleration.

v(t) = 8

a(t) = 0

When the position is a first order function, the velocity will be constant and the accerelation is zero.^{2}

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.^{3}

v(t) = 3t^{2}

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.

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) = 3tv(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) = tv(t) = 3t

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.