Position to velocity

This page provides some examples of how velocity (or speed) is calculated if the position formula is known. The position can be calculated by differentiating the position equation.

v(t) = velocity (speed)

v(t) = 0

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

v(t) = 4

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

v(t) = 4t

In this case, the position is a second order function. This means that the velocity is a first order function.^{3}

v(t) = 15t^{2}

When the position is a third order function, the velocity is a second order function.

Physics equations

x(t) = position v(t) = velocity (speed)

v(t) = x'(t)

Example 1

x(t) = 12 v(t) = 0

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

Example 2

x(t) = 4t v(t) = 4

When the position is a first order function, the velocity will be constant.

Example 3

x(t) = 2tv(t) = 4t

In this case, the position is a second order function. This means that the velocity is a first order function.

Example 4

x(t) = 5tv(t) = 15t

When the position is a third order function, the velocity is a second order function.