Displacement, velocity and acceleration

Vector quantity

A vector quantity is characterised by a magnitude and a direction. It is represented mathematically by a vector.

Magnitude of the quantity

Length of the vector

Direction of the quantity

Direction of the vector, i.e.vthe orientation of the line along which it acts, together with the way it points along that line.

What is the difference between a physical quantity and its mathematical representation?

The main difference between a physical quantity and its mathematical representation lies in the fact that a physical quantity is always expressed in a system of units.

Speed

The speed is defined as the ratio of the displacement s ro the unit of time; in other words it represents the variation of the position delta s over a certain duration delta t.

Acceleration

The acceleration is defined as the variation of the velocity per unit of time.

Gradient

The gradient, often denoted as grad, is a mathematical function defined as:

In the case of (s-t) diagram, the gradient corresponds to the speed:

Gradient = s/t = v

In the case of a (v-t) diagram, the gradient represents the acceleration:

Gradient = v/t = a