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How Science works: Graphs

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**About different types of graphs, **

Learning Objectives You should learn : About different types of graphs, How to draw them when you are doing your practical work, How to interpret the different shapes.

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**When should I draw a bar-chart…? …and when should I draw a line-graph?**

Drawing a graph When should I draw a bar-chart…? …and when should I draw a line-graph?

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**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:

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

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

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**5 steps in drawing a graph**

1. Choose simple scales. For example: 1 large square = 1 newton (1 N) or 1 large square = 2 N, or 5 N, or 10 N But 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.

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**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’

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**5 steps in drawing a graph**

2. Plot the points neatly. To mark the points we usually use an X x x x Usually you need 5 or more points for the graph. x x x Re-check each one before your next step.

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**5 steps in drawing a graph**

If the points form a straight line… …draw the best straight line through them x ‘line of best fit’ Check that it looks the best straight line.

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**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’.

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**5 steps in drawing a graph**

5. If a point is not on the line… …use your apparatus to check this measurement again x This is called an anomalous point. You can decide to ignore anomalous points.

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**5 steps in drawing a graph**

In summary: Choose good scales, with the dependent variable on the y-axis Plot the points carefully Draw a line of best fit using a ruler for a straight line graph, or draw free-hand for a curved graph Check anomalous points.

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Types of graphs Let’s look at some examples of graphs

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**Types of graphs 1 A straight line graph:**

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

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Types of graphs A special case is when the straight line goes through the origin : In this case the two quantities are directly proportional. If one doubles, then the other one also doubles. origin

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

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**Types of graphs 2 Example 1:**

the extension of a spring against the weight on it. extension weight

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**Types of graphs 2 Example 2:**

the current in a resistor against the p.d. across it. current voltage This illustrates Ohm’s Law.

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**Types of graphs 3 A curved graph, rising :**

The dependent variable rises quickly at first and then more slowly Here are some examples:

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**Types of graphs 3 Example 1:**

the velocity of a falling object against the time. velocity time Eventually the object will reach its terminal velocity.

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**Types of graphs 3 Example 2:**

the current in a filament lamp against the p.d. current voltage

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**Types of graphs 4 A curved graph, falling :**

The dependent variable falls quickly at first and then more slowly Here are some examples:

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**Types of graphs 4 Example 1:**

the activity of a radioactive source against the time. activity time The time to fall to half is called the half-life.

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**Types of graphs 4 Example 2:**

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

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**Know how to draw a line-graph correctly, **

Learning Outcomes You should now: 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.

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DISTANCE-TIME GRAPHS Plotting distance against time can tell you a lot about motion. Let's look at the axes:

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**Time is always plotted on the X-axis (bottom of the graph)**

Time is always plotted on the X-axis (bottom of the graph). The further to the 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 the graph, the further from the start.

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**Time is increasing to the right, but its **

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.

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**Constant speed is shown by straight lines on a graph.**

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.

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**Both lines are straight, so both speeds are constant.**

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

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Graphs that show acceleration look different from those that show constant speed. Time is increasing to the right, and distance The 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.

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

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.

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SPEED-TIME GRAPHS Speed-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!

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**This graph shows increasing speed. The moving object is accelerating.**

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**This graph shows decreasing speed. The moving object is decelerating.**

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**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.

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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.

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Graph Slope Area under the graph Position vs. time velocity Velocity vs. time acceleration displacement Acceleration vs. time Change in velocity

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