Distance Time Graphs (5) - SANDSMATHS
Distance Time Graphs (5) A distance time graph is a way of visually representing a journey on a graph. The distance time graph below shows the progress of a cyclist and a motorist between Perth and Lochearnhead (60 km from Perth). Both travelled along the same route. Distance from Perth (km) Cyclist and Motorist 60 55 50 45 40 35 30 25 20 15 10 5 0 Cyclist Motorist 17:00 16:30 16:00 15:30 15:00 14:30 14:00 13:30 13:00 Time of Day
In this type of graph, the time is along the bottom (the horizontal or the X axis). The distance from the starting point (Perth) is up the side (the vertical or the Y axis). In the past students told me they understood distance time graphs once they started using them to answer questions (rather than reading about them). Here are some questions to try. When did the cyclist leave Perth? Q2 How far away from Perth was the cyclist at 14:45? Q3 When did the motorist leave Perth? Q4 How far away from Perth was the motorist at 14:30? Q1 Q1 13:30 ANSWERS Q2 20km Q3 14:00 Q4 about 25km
Direction of travel In any distance time graph you can get information about the direction someone was travelling by the slope of the line (you’ll see the word “gradient”, it means slope). If the line is sloping up, the person is travelling away from the starting point. If the line is sloping down, the person is travelling back towards the starting point. Stopping and restarting If the line is FLAT, they have stopped moving. Here are more questions to try (instead of more explanation): The cyclist stopped for a rest at 16:00. Q5 How far away from Perth were they when they stopped? Q6 How many minutes did they stop for? The motorist reached Lochearnhead at 15:15. . Q7 How long did the journey from Perth take? Q8 How long did they stay in Lochearnhead before heading back? Q9 Which journey was quicker, there or back?
ANSWERS Q5 35 km Q6 30 mins (the line is FLAT from 16:00 to 16:30) Q7 75 mins (an hour and a quarter) they left at 14:00, arrived 15:15 Q8 60 mins (an hour) from 15:15 to 16:15 Q9 The journey back to Perth was quicker Journey there from Perth 75 mins Journey back to Perth 45 mins (from 16:15 to 17:00) The slope of the line can tell you the speed The slope of the line can tell you the speed someone was travelling at. The steeper the slope, the faster they were travelling. If you’ve got a section that’s a straight line, you can actually work out the average speed. The cyclist was 35km from Perth when they stopped for a rest at 16:00. They restarted at 16:30 and by 17:00 they were 50km from Perth. That means they travelled 15km (50 – 35) in half an hour (from 16:30 to 17:00) Their average speed in “km per hour” will be twice that, 30km per hour.
What was the average speed of the cyclist on the journey: Q10 in the hour between 13:30 and 14:30? Q11 in the hour between 14:45 and 15:45? What was the average speed of the motorist on the journey: Q12 from Perth to Lochearnhead in the hour between 14:00 and 15:00? Q13 from Lochearnhead back to Perth in the half hour between 16:30 and 17:00?
ANSWERS Q10 About 16 km per hour The cyclist leaves Perth at 13:30 At 14:30 they’re about 16 km from Perth They’ve travelled 16 km in an hour Q11 About 12 km per hour The cyclist is 20 km from Perth at 14:45 At 15:45 they’re about 32 km from Perth They’ve travelled 12 km in an hour (32 - 20 12). Q12 About 48 km per hour The motorist leaves Perth at 14:00 At 15:00 they’re about 48 km from Perth They’ve travelled 48 km in an hour Q13 About 80 km per hour The motorist is 40 km from Perth at 16:30 At 17:00 they’re back in Perth. They’ve travelled 40 km in half an hour The speed in “km per hour” is twice that.
The motorist and the cyclist used the same route and you can tell from the distance time graph that the motorist would have seen the cyclist on the road twice, once on the way there and once on the way back (the lines cross twice). The first time was on the journey to Lochearnhead about 12km from Perth. Q14 What time did this happen? . The motorist passed the cyclist again when they were travelling back to Perth (the cyclist was still heading to Lochearnhead). Q15 What time did this happen? . Q16 How far from Perth did this happen? . About 36 km from Perth Q16 Just after 16:30 (about 16:35) Q15 14:15 Q14 ANSWERS
Time of Day Cyclist and Motorist Cyclist Motorist Distance Time Graphs (5) A distance time graph is a way of visually representing a journey on a graph. The distance time graph below shows the progress of a cyclist and a motorist between Perth and Lochearnhead (60 km from Perth). Both travelled along the same route.
Math 6 NOTES Name _ Types of Graphs: Different Ways to Represent Data Line Graphs Line graphs are used to display continuous data. Line graphs can be useful in predicting future events when they show trends over time. Bar Graphs Bar graphs are used to display categories of data.
difierent characterizations of pushdown graphs also show the limited expres-siveness of this formalism for the deflnition of inflnite graphs. Preflx Recognizable Graphs. The equivalence of pushdown graphs to the graphs generated by preflx rewriting systems on words leads to a natural extension of pushdown graphs.
plays (tables, bar graphs, line graphs, or Venn diagrams). [6] S&P-2 The student demonstrates an ability to analyze data (comparing, explaining, interpret-ing, evaluating; drawing or justifying conclusions) by using information from a variety of dis-plays (tables, bar graphs, line graphs, circle graphs, or Venn diagrams). Materials:
to address outnumber the available graphs. This paper demonstrates how to create your own ad. vanced graphs by intelligently combining existing graphs. This presentation explains how you can create the following types of graphs by combining existing graphs: a line-based graph that shows a line for each
Sometimes describing motion is hard to do with words. Graphs make it easier to picture. Distance-Time Graphs On your paper, graph the following: d (m) t (s) 0 0 5 7 . Aka: position-time graphs Like distance time graphs, but with direction (can be either positive or negative).
possible times and distances for a selected distance-time graph. They will also draw their own distance-time graphs to show different stories presented to them. 8. Flow of the Unit Introduction to Co-ordinate Geometry # of lesson periods 1 Diagnostic test (distance - time graph) to reveal the students' current understandings & difficulties.
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INTRODUCTION 5 562, 579, 582, 585, 591, 592, 610). Population genetics, for example, identifies the conditions—selection pressures, mutation rates, population
