# 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 (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).

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.

Didn't find what you are looking for on this page? Try search:

### Online Algebra Solver

This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)

Play a math game.

(Well, not really a math game, but each game was made using math...)

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

### Math Lessons on DVD

Easy to understand math lessons on DVD. See samples before you commit.