# Displacement, Speed, and Acceleration

This section introduces displacement, speed, and acceleration by looking at the meanings and the units used as well as the relationships between each term.

## Displacement

Displacement refers to the amount by which the position of a measurement target moves.

This amount will represent different things in different situations. For example, for stationary targets, the displacement amount represents how much the target has changed in size. For moving targets, the displacement amount represents how much the target has moved. For vibrating measurement targets, the displacement amount represents the amplitude.

## Speed

Speed refers to the amount of displacement for a given time unit for an object.

In general, the speed can be determined by dividing the displacement by the elapsed time. For non-constant speeds, determining how detailed the elapsed time can be divided is important for this calculation.

## Acceleration

Acceleration refers to the amount of change in speed per unit of time.

The most commonly used units are “m/s^{2}” and “G” (where 1 G = 9.8 m/s^{2}).

The magnitude of vibration can also be expressed as acceleration, for which “Gal” (“cm/s^{2}”) is often used.

## Relationships between displacement, speed, and acceleration

The following correlations exist between acceleration, velocity, and displacement.

Differentiation of the displacement gives the speed, while differentiation of the speed gives the acceleration.

Integration of the acceleration gives the speed, and integration of the speed gives the displacement.

For discrete data sampled over a fixed period, the speed and acceleration can be calculated from the displacement data as shown below.

Speed V_{n} = (Displacement X_{n} – Displacement X_{n-m}) / m

Acceleration A_{n} = (Displacement V_{n} – Displacement V_{n-m}) / m

Although capturing more sudden changes in speed and acceleration is possible with a smaller m value, variations in the displacement data will have a greater effect.