2About different types of graphs, Learning ObjectivesYou should learn :About different types of graphs,How to draw them when you are doing your practical work,How to interpret the different shapes.
3When should I draw a bar-chart…? …and when should I draw a line-graph? Drawing a graphWhen should I draw a bar-chart…?…and when should I draw a line-graph?
4Drawing 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:
5What is the best way to draw a line-graph? Drawing a graphWhat is the best way to draw a line-graph?
65 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 NChoose a scale that will make your graphuse most of the sheet of paper.
75 steps in drawing a graph 1. Choose simple scales.Put the dependent variable on the ‘y-axis’andthe independent variable on the ‘x-axis’
85 steps in drawing a graph 2. Plot the points neatly.To mark the points we usually use an XxxxUsually you need 5 or more points for the graph.xxxRe-check each one before your next step.
95 steps in drawing a graph If the points form a straight line……draw the best straight line through themx‘line of best fit’Check that it looks the best straight line.
105 steps in drawing a graph 4. If the points form a curve……draw a free-hand curve of best fitDo not join the points like a ‘dot-to-dot’.
115 steps in drawing a graph 5. If a point is not on the line……use your apparatus to check this measurement againxThis is called an anomalous point.You can decide to ignore anomalous points.
125 steps in drawing a graph In summary:Choose good scales, with the dependent variable on the y-axisPlot the points carefullyDraw a line of best fit using a ruler for a straight line graph,or draw free-hand for a curved graphCheck anomalous points.
13Types of graphsLet’s look at some examples of graphs
14Types of graphs 1 A straight line graph: lengthlengthweightweightAn example would be the length of a spring against the weight on it.
15Types of graphsA special case is when the straight line goes through the origin :In this case thetwo quantities aredirectly proportional.If one doubles, then the other one also doubles.origin
16Types of graphsIf you think your graph should go through the origin, then draw it exactly through the origin.
17Types of graphs 2 Example 1: the extension of a spring against the weight on it.extensionweight
18Types of graphs 2 Example 2: the current in a resistor against the p.d. across it.currentvoltageThis illustrates Ohm’s Law.
19Types of graphs 3 A curved graph, rising : The dependent variable rises quickly at firstand then more slowlyHere are some examples:
20Types of graphs 3 Example 1: the velocity of a falling object against the time.velocitytimeEventually the object will reach its terminal velocity.
21Types of graphs 3 Example 2: the current in a filament lamp against the p.d.currentvoltage
22Types of graphs 4 A curved graph, falling : The dependent variable falls quickly at firstand then more slowlyHere are some examples:
23Types of graphs 4 Example 1: the activity of a radioactive source against the time.activitytimeThe time to fall to half is called the half-life.
24Types of graphs 4 Example 2: the rate of change is shown by the gradient of the graph.accelerationtime
25Know how to draw a line-graph correctly, Learning OutcomesYou 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.
26DISTANCE-TIME GRAPHS Plotting distance against time can tell you a lot about motion. Let's look at the axes:
27Time 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.
28Time 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 itsdistance does not change. It is notmoving. We say it is At Rest.
29Constant 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.
30Both 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.
31Graphs 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.
32A 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.
34SPEED-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!
35This graph shows increasing speed. The moving object is accelerating.
36This graph shows decreasing speed. The moving object is decelerating.
37What 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 greateracceleration.
38Summary: 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.