How Science works:Graphs About different types of graphs, How to draw them when you are doing your practical work, How to interpret the different shapes.

How Science works:

GraphsGraphs

• About different types of graphs,

• How to draw them when you are doing your practical work,

• How to interpret the different shapes.

Learning Objectives

You should learn :

Drawing a graphWhen should

I draw a bar-chart…?

…and when should I draw a line-graph?

Drawing a graph

Look at the table of your results:

If this column has

• only certain fixed values,use a bar-chart:

• a continuous range of values,use a line-graph:

Drawing a graph

What is the best way to draw a line-graph?

5 steps in drawing a graph

1. Choose simple scales.

For example:1 large square = 1 newton (1 N)or1 large square = 2 N, or 5 N, or 10 NBut never choose an awkward scale, like 1 square = 3 N or 7 N

Choose a scale that will make your graph use most of the sheet of paper.

5 steps in drawing a graph

1. Choose simple scales.

Put the dependent variable on the ‘y-axis’

and the independent variable on the ‘x-axis’

5 steps in drawing a graph

2. Plot the points neatly.

To mark the points we usually use an X

x

xx

x

xx

Re-check each one before your next step.

Usually you need 5 or more points for the graph.

5 steps in drawing a graph

3. If the points form a straight line…

…draw the best straight line through them

x

xx

x

xx

Check that it looks the best straight line.

‘line of best fi

t’

5 steps in drawing a graph

4. If the points form a curve…

…draw a free-hand curve of best fit

Do not join the points like a ‘dot-to-dot’.

5 steps in drawing a graph

5. If a point is not on the line…

…use your apparatus to check this measurement again

You can decide to ignore anomalous points.

This is called an anomalous point.

x

x

x

xx

x

5 steps in drawing a graph

In summary:

1. Choose good scales,with the dependent variable on the y-axis

2. Plot the points carefully

3. Draw a line of best fitusing a ruler for a straight line graph,

4. or draw free-hand for a curved graph

5. Check anomalous points.

Let’s look at some examples of graphs

Types of graphs

A straight line graph:

Types of graphs 1

An example would be the length of a spring against the weight on it.

weight

leng

th

leng

th

weight

Types of graphs 2

A special case is when the straight line goes through the origin :

origin

In this case the two quantities are directly proportional.

If one doubles, then the other one also doubles.

Types of graphs 2

If you think your graph should go through the origin, then draw it exactly through the origin.

Types of graphs 2

Example 1:

the extension of a springagainst the weight on it.

exte

nsi

on

weight

Types of graphs 2

Example 2:

the current in a resistoragainst the p.d. across it.

curr

en

t

voltage

This illustrates Ohm’s Law.

Types of graphs 3

A curved graph, rising :

The dependent variable rises quickly at first and then more slowly

Here are some examples:

Types of graphs 3

Example 1:

the velocity of a falling objectagainst the time.

velo

city

time

Eventually the object will reach its terminal velocity.

Types of graphs 3

Example 2:

the current in a filament lampagainst the p.d.

curr

en

t

voltage

Types of graphs 4

A curved graph, falling :

The dependent variable falls quickly at first

and then more slowly

Here are some examples:

Types of graphs 4

Example 1:

the activity of a radioactive sourceagainst the time.

act

ivit

y

time

The time to fall to half is called the half-life.

Types of graphs 4

Example 2:

the rate of change is shown by the gradient of the graph.

acc

ele

rati

on

time

• Know how to draw a line-graph correctly,

• Be able to give examples of graphs with different shapes,

• Be able to interpret graphs with different shapes.

Learning Outcomes

You should now:

DISTANCE-TIME GRAPHSPlotting distance against time can tell you a lot

about motion. Let's look at the axes:

Time is always plotted on the X-axis(bottom of the graph). The further tothe right on the axis, the longer the

time from the start.Distance is plotted on the Y-axis (side

of the graph). The higher up thegraph, the further from the start.

If an object is not moving, a horizontal line is shown on a distance-time graph.

Time is increasing to the right, but its

distance does not change. It is not

moving. We say it is At Rest.

If an object is moving at a constant speed, it means it has the same increase in

distance in a given time:

Time is increasing to the right, and distance is

increasing constantly with time. The object moves at a

constant speed.

Constant speed is shown by straight lines on a

graph.

Let’s look at two moving objects:Both of the lines in the graph show that each object moved the same distance,

but thesteeper dashed line got there before the

other one:A steeper line indicates a larger distance moved in a given time. In other words,

higher speed.

Both lines are straight, so both speeds are constant.

Graphs that show acceleration look different from those that show constant

speed.Time is increasing to the right, and

distanceThe line on this graph is curving upwards. This shows an increase in speed, since the line is

getting steeper:

In other words, in a given time, the distance the

object moves is change (getting larger). It is

accelerating.

Summary:

A distance-time graph tells us how far an object has moved with time.

• The steeper the graph, the faster the motion.

• A horizontal line means the object is not changing its position - it is not moving, it is at rest.

• A downward sloping line means the object is returning to the start.

SPEED-TIME GRAPHSSpeed-Time graphs are also called Velocity Time

graphs.Speed-Time graphs look much like Distance-Time

graphs. Be sure to read the labels!! Time is plotted on the X-axis. Speed or velocity is plotted

on the Y-axis.A straight horizontal line on a speed-time graph means that speed is constant. It is not changing over time. A straight line does not mean that the

object is not moving!

This graph shows increasing speed.

The moving object is accelerating.

This graph shows decreasing speed.

The moving object is decelerating.

What about comparing two moving objects at the

same time?Both the dashed and solid

line show increasing speed.

Both lines reach the same top speed, but the solid one

takes longer.

The dashed line shows a greater

acceleration.

Summary:A speed - time graph shows us how the speed of a moving object changes with

time.• The steeper the graph, the greater the

acceleration.• A horizontal line means the object is

moving at a constant speed.• A downward sloping line means the

object is slowing down.

Graph Slope Area under the graph

Position vs. time

velocity ---------

Velocity vs. time

acceleration displacement

Acceleration vs. time

---------- Change in velocity