1. © T Madas

2. Marc started from his house at 9 a.m. cycling at constant speed to Andy’s house, 7 km away. He arrived there one hour later. Marc stayed at Andy’s for 1½ hours. He started cycling back home. Half hour into his return journey he stopped at Elli’s house that lives 4 km from his house. He stayed at Elli’s for half an hour. He continued cycling home at constant speed arriving back at 2 p.m. Graphs which show how the distance of an object from a starting point changes with time, are called distance-time graphs or simply travel-graphs Draw a distance-time graph for this information

3. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km Time always plotted on the x axis

4. © T Madas Marc started from his house at 9 a.m. cycling at constant speed to Andy’s house, 7 km away. He arrived there one hour later. Marc stayed at Andy’s for 1½ hours. He started cycling back home. Half hour into his return journey he stopped at Elli’s house that lives 4 km from his house. He stayed at Elli’s for half an hour. He continued cycling home at constant speed arriving back at 2 p.m. Graphs which show how the distance of an object from a starting point changes with time, are called distance-time graphs or simply travel-graphs Draw a distance-time graph for this information

5. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km Time always plotted on the x axis

6. © T Madas Marc started from his house at 9 a.m. cycling at constant speed to Andy’s house, 7 km away. He arrived there one hour later. Marc stayed at Andy’s for 1½ hours. He started cycling back home. Half hour into his return journey he stopped at Elli’s house that lives 4 km from his house. He stayed at Elli’s for half an hour. He continued cycling home at constant speed arriving back at 2 p.m. Graphs which show how the distance of an object from a starting point changes with time, are called distance-time graphs or simply travel-graphs Draw a distance-time graph for this information

7. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km Time always plotted on the x axis

8. © T Madas Marc started from his house at 9 a.m. cycling at constant speed to Andy’s house, 7 km away. He arrived there one hour later. Marc stayed at Andy’s for 1½ hours. He started cycling back home. Half hour into his return journey he stopped at Elli’s house that lives 4 km from his house. He stayed at Elli’s for half an hour. He continued cycling home at constant speed arriving back at 2 p.m. Graphs which show how the distance of an object from a starting point changes with time, are called distance-time graphs or simply travel-graphs Draw a distance-time graph for this information

9. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km Time always plotted on the x axis

10. © T Madas Marc started from his house at 9 a.m. cycling at constant speed to Andy’s house, 7 km away. He arrived there one hour later. Marc stayed at Andy’s for 1½ hours. He started cycling back home. Half hour into his return journey he stopped at Elli’s house that lives 4 km from his house. He stayed at Elli’s for an half hour. He continued cycling home at constant speed arriving back at 2 p.m. Graphs which show how the distance of an object from a starting point changes with time, are called distance-time graphs or simply travel-graphs Draw a distance-time graph for this information

11. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km Time always plotted on the x axis

12. © T Madas Marc started from his house at 9 a.m. cycling at constant speed to Andy’s house, 7 km away. He arrived there one hour later. Marc stayed at Andy’s for 1½ hours. He started cycling back home. Half hour into his return journey he stopped at Elli’s house that lives 4 km from his house. He stayed at Elli’s for half an hour. He continued cycling home at constant speed arriving back at 2 p.m. Graphs which show how the distance of an object from a starting point changes with time, are called distance-time graphs or simply travel-graphs Draw a distance-time graph for this information

13. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km Time always plotted on the x axis What do the “flat” parts of the graph represent? Flat = not travelling/a stop

14. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km Time always plotted on the x axis What do the “uphill” parts of the graph represent? Flat = not travelling/a stop Uphill = travelling away

15. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km Time always plotted on the x axis What do the “down hill” parts of the graph represent? Flat = not travelling/a stop Uphill = travelling away Downhill = travelling back

16. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km What was Marc’s speed in cycling from his house to Andy’s house? speed = distance time 7kmperhour 7km/h in 1 hour7 km 7 1 == =

17. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km What was Marc’s speed in cycling from Andy’s house to Elli’s house? 6kmperhour 6km/h in ½ hour3 km 3 ½ == = in ½ hour3 km in 1 hour6 km 6km/h= speed = distance time

18. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km What was Marc’s speed in cycling from Ellis’s house back home? 2.67kmperhour 2.67km/h in 1½ hour4 km 4 1.5 =≈ ≈ in 1½ hour4 km in 3 hours8 km ÷ 8 = 3 8 3 = 2 2 3 km/h 2.67km/h≈ speed = distance time

19. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km What was Marc’s average speed for the entire journey? 2.8kmperhour 2.8km/h in 5 hours14 km 14 5 == = 2.8km/h= speed = distance time km 14 28 2.8 Hours 5 10 1

20. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km The speed for each section is also represented by the slope of each section. 1 7 7 km/h ½ 3 -6 km/h 1.5 4 -2.67 km/h Gradient = Speed [in a distance-time graph] The steeper the line, the greater the speed speed = distance time

21. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 876543210876543210 Time Distance from home in Km 7 km/h -6 km/h -2.67 km/h Gradient = Speed [in a distance-time graph] The steeper the line, the greater the speed speed = distance time The speed for each section is also represented by the slope of each section.

22. © T Madas Graphs which show how the distance of an object from a starting point changes with time, are called distance-time graphs or simply travel-graphs Time is always plotted on the x axis the “flat” parts of the graph indicate stops (no motion) the “uphill” parts indicate travelling away from the starting point the “downhill” parts indicate travelling back to the starting point To find the speed we use: The speed in a distance-time graph is given by the slope (also called gradient) of a line Distance-Time Graphs Summary speed = distance time

23. © T Madas

24. 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 240 220 200 180 160 140 120 100 80 60 40 20 Time in hours Distance from London in miles A sales rep drove from London to Manchester, stopping on the way at Birmingham. After his meeting in Manchester, he drove straight to London without a break. His entire journey is shown in the graph below: Q1 How many miles is Birmingham from London? 120 miles

25. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 240 220 200 180 160 140 120 100 80 60 40 20 Time in hours Distance from London in miles A sales rep drove from London to Manchester, stopping on the way at Birmingham. After his meeting in Manchester, he drove straight to London without a break. His entire journey is shown in the graph below: Q2 How long did he stop in Birmingham for? half an hour

26. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 240 220 200 180 160 140 120 100 80 60 40 20 Time in hours Distance from London in miles A sales rep drove from London to Manchester, stopping on the way at Birmingham. After his meeting in Manchester, he drove straight to London without a break. His entire journey is shown in the graph below: Q3 How far is Manchester from Birmingham? 90 miles

27. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 240 220 200 180 160 140 120 100 80 60 40 20 Time in hours Distance from London in miles A sales rep drove from London to Manchester, stopping on the way at Birmingham. After his meeting in Manchester, he drove straight to London without a break. His entire journey is shown in the graph below: Q4 How long did the entire journey take 9 hours

28. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 240 220 200 180 160 140 120 100 80 60 40 20 Time in hours Distance from London in miles A sales rep drove from London to Manchester, stopping on the way at Birmingham. After his meeting in Manchester, he drove straight to London without a break. His entire journey is shown in the graph below: Q5 What was the average speed for the driving parts of journey? average speed = total distance total time = 420 6.5 ≈ 65 miles/hour

29. © T Madas 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 240 220 200 180 160 140 120 100 80 60 40 20 Time in hours Distance from London in miles A sales rep drove from London to Manchester, stopping on the way at Birmingham. After his meeting in Manchester, he drove straight to London without a break. His entire journey is shown in the graph below: Q6 What was the speed for each part of the journey? 2 120 60 mph 2 90 45 mph 2½2½ 210 84 mph speed = distance time Miles 210 420 840 84 Hours 2½2½ 5 10 1

30. © T Madas

31. 0 1 2 3 4 5 6 7 8 9 10 11 Time in seconds 100 90 80 70 60 50 40 30 20 10 Distance in metres The distance-time graph below shows a 100 metre race for 3 sprinters labelled as A, B and C. 1. Who won the race and what was the winning time. 2. How many seconds behind the winner was the runner up? 3. Explain what happened 10 seconds into the race. 4. What is a possible explanation for the run of sprinter C ? A C A : 100 m in 10.5 sec B : 100 m in 11 sec C : did not finish 1.10.5 sec 2.Half a second 3.A overtook B 4.Possibly a muscle pull B

32. © T Madas

33. 120 100 80 60 40 20 0 Time in hours Distance from London in km ¼ ½ ¾ 1 1¼ 1½ 1¾ 2 The travel-graph below shows a car journey from London to Gatwick Airport. The 1 st part of the journey to Croydon took 1 hour, due to traffic 1.Calculate the speed for the London-Croydon section 2.Calculate the speed for the Croydon-Gatwick section 3.Calculate the average speed for the entire journey speed = distance time 1 40 40 km/h ½ 80 160 km/h

34. © T Madas 120 100 80 60 40 20 0 Time in hours Distance from London in km ¼ ½ ¾ 1 1¼ 1½ 1¾ 2 The travel-graph below shows a car journey from London to Gatwick Airport. The 1 st part of the journey to Croydon took 1 hour, due to traffic 1.Calculate the speed for the London-Croydon section 2.Calculate the speed for the Croydon-Gatwick section 3.Calculate the average speed for the entire journey 1½1½ 120 80 km/h average speed = total distance total time = 120 1.5 = 80 km/h km 120 240 80 Hours 1½1½ 3 1 or

35. © T Madas

36. The distance – time graph shown opposite describes Jon’s journey. Tick the correct boxes of the 4 statements which describe part A, part B and part C of his journey. time distance A B C … was walking in a North-East direction … was walking back to his starting point … was walking at his fastest … was walking at constant speed … took some rest … was walking uphill … was walking slower and slower … was walking faster and faster CBAOn this part, Jon …

37. © T Madas

38. 10 20 30 40 50 60 40 35 30 25 20 15 10 5 0 Time (seconds) Distance from the start (metres) The following distance-time graph shows Lee’s egg and spoon race, from the starting line to the end of the track and back to the starting line. 1.What was the total distance run? 70 metres 2.How many times did Lee drop the egg? Twice 3.What was Lee’s average speed? approx 1.17 m/s 4.Calculate Lee’s speed at various parts of the race 35 metres to the end of the track and 35 metres back average speed = total distance total time = 70 60 ≈ 1.17 m/s

39. © T Madas 10 20 30 40 50 60 40 35 30 25 20 15 10 5 0 Time (seconds) Distance from the start (metres) The following distance-time graph shows Lee’s egg and spoon race, from the starting line to the end of the track and back to the starting line. 1.What was the total distance run? 70 metres 2.How many times did Lee drop the egg? Twice 3.What was Lee’s average speed? approx 1.17 m/s 4.Calculate Lee’s speed at various parts of the race speed = distance time 10 20 2 m/s 15 1 m/s 5 25 5 m/s 20 10 ½ m/s

40. © T Madas

41. Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 1. Plot a distance-time graph 2. What distance do the joggers cover? 3. After how many minutes does jogger B overtake jogger A for the first time? 4. After how many metres does jogger A overtake jogger B ?

42. Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 2800 2400 2000 1600 1200 800 400 0 2 4 6 8 10 12 14 16 18 20 22 24 min metres A B

43. © T Madas Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 1. Plot a distance-time graph 2. What distance do the joggers cover? 3. After how many minutes does jogger B overtake jogger A for the first time? 4. After how many metres does jogger A overtake jogger B ?

44. © T Madas Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 2800 2400 2000 1600 1200 800 400 0 2 4 6 8 10 12 14 16 18 20 22 24 min metres A B

45. © T Madas Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 1. Plot a distance-time graph 2. What distance do the joggers cover? 3. After how many minutes does jogger B overtake jogger A for the first time? 4. After how many metres does jogger A overtake jogger B ?

46. © T Madas Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 2800 2400 2000 1600 1200 800 400 0 2 4 6 8 10 12 14 16 18 20 22 24 min metres A B

47. © T Madas Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 1. Plot a distance-time graph 2. What distance do the joggers cover? 3. After how many minutes does jogger B overtake jogger A for the first time? 4. After how many metres does jogger A overtake jogger B ?

48. © T Madas Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 2800 2400 2000 1600 1200 800 400 0 2 4 6 8 10 12 14 16 18 20 22 24 min metres A B

49. © T Madas Two joggers start from the same point and run the same distance in 21 minutes as follows: Jogger A: He runs every 800 metres in 5 minutes followed by a 3 minute rest Jogger B: She runs for 21 minutes at constant speed. 1. Plot a distance-time graph 2. What distance do the joggers cover? 3. After how many minutes does jogger B overtake jogger A for the first time? 4. After how many metres does jogger A overtake jogger B ?

50. © T Madas

51. 0 1 2 3 4 5 6 7 8 9 10 11 Time in seconds 100 90 80 70 60 50 40 30 20 10 Distance in metres from Nick’s spot A thief seeking to avoid capture runs through a park with a speed of 6 m/s As he runs past Nick, Nick sets in pursuit of the thief, on his mountain bike. Nick cycles at a speed of 9 m/s but took 3 seconds to react and get on his bike. Assuming that Nick did not see the thief until he was running past him: 1.Draw a distance time graph showing this information. 2.Hence find how many seconds does Nick have to cycle until he draws level with the thief

52. © T Madas A thief seeking to avoid capture runs through a park with a speed of 6 m/s As he runs past Nick, Nick sets in pursuit of the thief, on his mountain bike. Nick cycles at a speed of 9 m/s but took 3 seconds to react and get on his bike. Assuming that Nick did not see the thief until he was running past him: 1.Draw a distance time graph showing this information. 2.Hence find how many seconds does Nick have to cycle until he draws level with the thief The thief’s speed is 6 m/s 1 sec 2 sec 3 sec 10 sec etc 6 m 12 m 18 m 60 m etc 0 1 2 3 4 5 6 7 8 9 10 11 Time in seconds 100 90 80 70 60 50 40 30 20 10 Distance in metres from Nick’s spot

53. © T Madas A thief seeking to avoid capture runs through a park with a speed of 6 m/s As he runs past Nick, Nick sets in pursuit of the thief, on his mountain bike. Nick cycles at a speed of 9 m/s but took 3 seconds to react and get on his bike. Assuming that Nick did not see the thief until he was running past him: 1.Draw a distance time graph showing this information. 2.Hence find how many seconds does Nick have to cycle until he draws level with the thief 1 sec 2 sec 3 sec 4 sec etc 9 m 18 m 27 m 36 m etc 0 1 2 3 4 5 6 7 8 9 10 11 Time in seconds 100 90 80 70 60 50 40 30 20 10 Distance in metres from Nick’s spot 4 sec 5 sec 6 sec 7 sec etc Nick’s speed is 9 m/s

54. © T Madas A thief seeking to avoid capture runs through a park with a speed of 6 m/s As he runs past Nick, Nick sets in pursuit of the thief, on his mountain bike. Nick cycles at a speed of 9 m/s but took 3 seconds to react and get on his bike. Assuming that Nick did not see the thief until he was running past him: 1.Draw a distance time graph showing this information. 2.Hence find how many seconds does Nick have to cycle until he draws level with the thief 0 1 2 3 4 5 6 7 8 9 10 11 Time in seconds 100 90 80 70 60 50 40 30 20 10 Distance in metres from Nick’s spot Nick had to cycle for 6 seconds How far from Nick’s spot did Nick draw level? Using the graph Using the thief’s speed Using Nick’s speed

55. © T Madas

56. Height in metres Time in seconds A ball is thrown vertically upwards and its height at subsequent times is recorded. The results were plotted in the graph below. 1. By drawing the tangents on this curve, estimate the speed of the ball at times t = 2 and t = 4. 2. What is the meaning of a negative gradient? 2.5 25.5 gradient = 25.5 2.5 = 10.2

57. © T Madas Height in metres Time in seconds A ball is thrown vertically upwards and its height at subsequent times is recorded. The results were plotted in the graph below. 1. By drawing the tangents on this curve, estimate the speed of the ball at times t = 2 and t = 4. 2. What is the meaning of a negative gradient? 2.5 -23.5 gradient = 25.5 2.5 = 10.2 gradient = -23.5 2.5 = -9.2 at t = 2 speed ≈ 10.2 m/s at t = 4 speed ≈ 9.2 m/s

58. © T Madas

59. The graph below shows a journey on a lift, starting at the ground floor and returning to the ground floor sometime later. Find the time the lift spent stationary and the time it spent moving Show that the lift is travelling faster when going down Calculate the average speed for the lift when moving in m/s, if floors are 3 metres apart Time ( seconds ) Floor Number 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 20 15 10 5 total time: 1 st stop: 2 nd stop: 3 rd stop: time stationary: time moving: 150 s 10 s 25 s 15 s 50 s 100 s

60. © T Madas The graph below shows a journey on a lift, starting at the ground floor and returning to the ground floor sometime later. Find the time the lift spent stationary and the time it spent moving Show that the lift is travelling faster when going down Calculate the average speed for the lift when moving in m/s, if floors are 3 metres apart Time ( seconds ) Floor Number 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 20 15 10 5 4 floors in 15 s 8 floors in 30 s 4 floors in 15 s 16 floors in 40 s 8 floors in 20 s 4 floors in 10 s

61. © T Madas The graph below shows a journey on a lift, starting at the ground floor and returning to the ground floor sometime later. Find the time the lift spent stationary and the time it spent moving Show that the lift is travelling faster when going down Calculate the average speed for the lift when moving in m/s, if floors are 3 metres apart Time ( seconds ) Floor Number 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 20 15 10 5 time moving: floors up: floors down: total floors: total distance: 100 s 16 32 96 m speed = distance time = 96 100 = 0.96 m/s

62. © T Madas