DISTANCE TIME GRAPHS Distance Time Graphs This is

DISTANCE TIME GRAPHS

Distance Time Graphs This is graph of a family car journey from home for a day at the beach. • • How long did it take to get there? How long did they stay? How far away was it? How long did it take to get back? GRAPH OF A DRIVE TO THE BEACH 100 90 80 Distance(km) Time and distance graph questions often appear on examinations. As the name suggests, the axes are time (usually on the X axis) and distance (usually on the Y axis). The distance of an object from its starting position is plotted against the time it takes to get there. 70 60 50 40 30 20 10 0 0 1 2 3 4 5 6 7 Time (hours) 8 9 10

Distance Time Graphs A CYCLE TRIP TO THE POST OFFICE Look at the journey on the right. It shows a cyclist’s journey from home to a post office and back. 1000 900 • How far away is the post office? • How long did the cyclist wait at the post office? • What do you think might be 300 metres away from the home? Why? 700 Distance(m) • How long did the journey take from home to the post office? 800 600 500 400 300 200 100 0 • If the cyclist left at 10: 35 AM what time would they get back home? 0 1 2 3 4 5 6 7 Time (minutes) 8 9 10

Distance Time Graphs A CYCLE TRIP TO THE POST OFFICE We can use time and distance graphs to work out average speeds between points on lines. 1000 900 Distance Travelled (m) Speed = Time Taken (s) We can now calculate the average speed between the two points. 300 ÷ 120 = 2. 5 m/s • What was the average speed between C and D? Was it faster? D 700 Distance(m) Between points A and B the bike travels 300 metres in 120 seconds (2 minutes) 800 600 500 400 C 300 B 200 100 0 A 0 1 2 3 4 5 6 7 Time (minutes) 8 9 10

Distance Time Graphs You can also compare the speeds of different objects by looking at their gradients (the angle of 100 the line) C 80 70 Distance(m) Car B travels 100 m in 5 seconds: 100÷ 5=20 m/s B 90 Here are some model rocket car predictions. Car A travels 100 m in 2 seconds: 100÷ 2=50 m/s A 60 50 40 Car C travels 100 m in 10 seconds: 100÷ 10=10 m/s 30 Steeper lines represent faster movement. 10 20 0 0 1 2 3 4 5 6 7 Time (second) 8 9 10

Distance Time Graphs In reality vehicles do not always move at the same speed and when they speed up we call this acceleration and when they slow down we call this deceleration. 90 80 Green is a period of acceleration – the speed Red is deceleration – the speed decreases over time. The black line represents the line of average speed between A and B 70 Distance(m) increases over time. B 100 60 50 40 30 20 10 A 0 0 1 2 3 4 5 6 7 Time (second) 8 9 10

Distance Time Graphs GRAPH SHOWING DIFFERENT TYPES OF MOVEMENT When looking at distance time graphs some journeys may not end up back at the destination. Sometimes the lines may be curved and the shape of the curve can tell us how something is changing. The red line show a journey with a stop and a return The green line shows acceleration, then deceleration and finally a stop some distance away 90 Steady, fast speed Stationary Getting slower 80 70 Distance(m) The blue line shows a fast, steady speed but no return. 100 60 Stationary Steady speed 50 40 Steady return to start 30 20 Getting faster 10 0 0 1 2 3 4 5 6 7 Time (seconds) 8 9 10

Distance Time Graphs MODEL ROCKET CAR – PREDICTED DISTANCE TIME GRAPH This is a typical distance time graph for a model rocket car. 30 Distance (METRES) 25 15 Using your knowledge, work in groups or teams to find mathematical questions you can ask using this graph, e. g. 10 • How far did it travel? 5 • Did its stop quickly? 20 0 0 250 500 750 1000 Time (MILLISECONDS) 1250 1500 2000 • When does it accelerate quickest?