# 1. Velocity (*s-t*) Graphs

### Example 1

This general graph represents the motion of a body travelling at constant velocity. The graph is linear (that is, a straight line).

Recall that linear equations have the general form

y=mx(wheremis a constant andxis a variable).

The number *m* is called the slope of the line (the vertical rise over the horizontal run).

In the above graph, we have the function:

displacement = velocity × time

or

s=v×t

Velocity is constant and time is a variable.

We note that the graph passes through `(0,0)` and has slope
*v*. The slope of the line tells us the velocity. We can
also write the velocity using delta notation:

`v=(Deltas)/(Deltat)` which means "change in displacement over change in time".

If we have a high velocity, the graph has a steep slope. If we have a low velocity the graph has a shallow slope (assuming the vertical and horizontal scale of each graph is the same).

High speed Low speed

### Example 2

A marathon runner runs at a constant `12` km/h.

a. Express her displacement travelled as a function of time.

b. Graph the motion for `0 ≤ t ≤ 4\ "h"`

## Displacement-time Graphs

### Example 3

This is the graph of a journey by sports car:

a. What is the velocity for each stage of the journey?

b. What is the average (**mean**) velocity for the whole
journey?

### Example 4

A particle in a magnetic field moves as follows:

Find the velocity for each part of the motion.

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