1. Velocity (`s`-`t`) Graphs

Example 1

Distance-time graph - constant speed

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 (where m is a constant and x is 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).

Distance-time graphs

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:

math expression

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:

math expression

Find the velocity for each part of the motion.

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