1. Dynamics 7 September 2015 Speed is defined as the distance travelled per unit time and has the units of m/s or ms -1.

2. Dynamics 7 September 2015 Distance, Speed and Time Speed = distance (in metres) time (in seconds) D TS 1)Dave walks 200 metres in 40 seconds. What is his speed? 2)Laura covers 2km in 1,000 seconds. What is her speed? 3)How long would it take to run 100 metres if you run at 10m/s? 4)Steve travels at 50m/s for 20s. How far does he go? 5)Susan drives her car at 85mph (about 40m/s). How long does it take her to drive 20km?

3. Dynamics 7 September 2015 Speed is defined as the distance travelled per unit time and has the units of m/s or ms -1. Velocity is speed in a given direction and has the same units as speed.

4. Dynamics 7 September 2015 Speed vs. Velocity Speed is simply how fast you are travelling… Velocity is “speed in a given direction”… This car is travelling at a speed of 20m/s This car is travelling at a velocity of 20m/s east

5. Dynamics 7 September 2015 Speed is defined as the distance travelled per unit time and has the units of m/s or ms -1. Velocity is speed in a given direction and has the same units as speed. To calculate speed we use the equation: Average speed = distance travelled/time taken = d/t Distance is measured in metres (m) and time is measured in seconds (s). The greater the distance travelled in a given time then the greater is the speed.

6. Dynamics 7 September 2015 A useful way to illustrate how the distance throughout a journey varies with time is to plot a DISTANCE AGAINST TIME graph. This gives us a visual representation of how the journey progressed and allows us to see quickly how long each stage of the journey took compared with the other stages. The steepness (gradient) will also give us the speed. The following graphs show how the shape of distance-time graphs may vary and how to interpret them.

7. Dynamics 7 September 2015 Distance Time 0 0 A BC AB- constant speed BC - stationary Gradient = rise/run = speed Rise Run Distance - Time Graphs

8. Dynamics 7 September 2015 DISTANCE is a SCALAR quantity and has size only but DISPLACEMENT is a VECTOR quantity and has size (or magnitude) and DIRECTION. 10 metres is a distance (size only) but 10 metres due south (size and direction) is a vector quantity. If we use DISPLACEMENT instead of distance then the graph will also give an indication of the direction taken with respect to its starting point.

9. Dynamics 7 September 2015 Displacement Time 0 0 AB - constant velocity (speed & direction) BC - stopped CD - Returning to its starting position at a constant velocity A BC D Distance - Time Graphs

10. Dynamics 7 September 2015 Distance Time 0 0 A B C D E Speed is changing at B, C & D (Decreasing) Stopped At B,C & D there is instantaneous change in speed Distance - Time Graphs

11. Dynamics 7 September 2015 Distance Time 0 0 Speed is Constantly Changing (In this case speed is decreasing) Rise Run  A Speed AT A = Rise/Run = Gradient of tangent AT A Distance - Time Graphs Tangent drawn at A

12. Dynamics 7 September 2015 Distance Time 0 0 Speed is constantly changing (Increasing) Rise Run  A Speed AT A = Rise/Run = Gradient of tangent AT A Distance - Time Graphs

13. Dynamics 7 September 2015 Distance-time graphs 40 30 20 10 0 20 40 60 80100 4) Diagonal line downwards = 3) Steeper diagonal line = 1)Diagonal line = 2) Horizontal line = Distance (metres) Time/s

14. Dynamics 7 September 2015 40 30 20 10 0 20 40 60 80 100 1)What is the speed during the first 20 seconds? 2)How far is the object from the start after 60 seconds? 3)What is the speed during the last 40 seconds? 4)When was the object travelling the fastest? Distance (metres) Time/s

15. Dynamics 7 September 2015 Distance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. (a)Plot a distance-time graph. (b)What was the snail’s speed before lunch? (c)What was the snail’s speed after lunch?

16. Dynamics 7 September 2015 Distance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s)

17. Dynamics 7 September 2015 Distance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 4 8 12 16 800160240

18. Dynamics 7 September 2015 Distance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 4 8 12 16 080160240

19. Dynamics 7 September 2015 Distance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 4 8 12 16 80160240

20. Dynamics 7 September 2015 Distance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 4 8 12 16 80160240

21. Dynamics 7 September 2015 Distance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 (a)See graph (b)Speed before lunch = initial gradient = rise/run = 8/80 = 0.1m/s 4 8 12 16 80160240

22. Dynamics 7 September 2015 Distance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 (a)See graph (b)Speed before lunch = initial gradient = rise/run = 8/80 = 0.1m/s (c)Speed after lunch = final gradient = rise/run = 8/120 = 0.067 m/s 4 8 12 16 80160240

23. Dynamics 7 September 2015 Distance - Time Graphs: Examples Consider a car starting from rest and its speed is increasing continuously. Distance (m) Time (s) 0 200 400 600 800 2004060

24. Dynamics 7 September 2015 Distance - Time Graphs: Examples Consider a car starting from rest and its speed is increasing continuously. Find the speed of the car at 40 seconds after the start of the journey. Distance (m) Time (s) 0 200 400 600 800 2004060

25. Dynamics 7 September 2015 Distance - Time Graphs: Examples Consider a car starting from rest and its speed is increasing continuously. Find the speed of the car at 40 seconds after the start of the journey. Distance (m) Time (s) 0 200 400 600 800 2004060

26. Dynamics 7 September 2015 Distance - Time Graphs: Examples Consider a car starting from rest and its speed is increasing continuously. Find the speed of the car at 40 seconds after the start of the journey. Distance (m) Time (s) 0 200 400 600 800 2004060 Speed at 40 seconds = gradient of tangent drawn at 40s = rise/run = 800/40 = 20 m/s 800 40

27. Dynamics 7 September 2015 Acceleration is defined as the change in velocity in unit time and has the units m/s/s or m/s 2 or ms -2 Acceleration is a vector quantity and so has size and direction. To calculate acceleration we use the equation: Average acceleration = change in velocity/time taken = (final velocity – initial velocity)/time taken = (v – u)/t Velocity is measured in metres per second (m/s) and time is measured in seconds (s). The greater the change in velocity in a given time then the greater is the acceleration. Velocity - Time Graphs

28. Dynamics 7 September 2015 Acceleration V-U TA Acceleration = change in velocity (in m/s) (in m/s 2 ) time taken (in s) 1)A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration? 2)A ball is dropped and accelerates downwards at a rate of 10m/s 2 for 12 seconds. How much will the ball’s velocity increase by? 3)A car accelerates from 10 to 20m/s with an acceleration of 2m/s 2. How long did this take? 4)A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration?

29. Dynamics 7 September 2015 A useful way to illustrate how the velocity throughout a journey varies with time is to plot a VELOCITY AGAINST TIME graph. This gives us a visual representation of how the journey progressed and allows us to see quickly how long each stage of the journey took compared with the other stages. The steepness (gradient) will also give us the ACCELERATION. The area under a velocity-time graph gives us the distance travelled. The following graphs show how the shape of velocity-time graphs may vary and how to interpret them. Velocity - Time Graphs

30. Dynamics 7 September 2015 Velocity Time 0 0 A B C AB- constant acceleration BC - constant velocity Gradient = rise/run = acceleration (m/s 2 ) Rise Run Velocity - Time Graphs

31. Dynamics 7 September 2015 Velocity Time 0 0 A - B constant acceleration B - C Stopped accelerating (velocity is constant) C - D constant deceleration A BC D Area under Graph = Total Distance Travelled Velocity - Time Graphs

32. Dynamics 7 September 2015 Velocity Time 0 0 A B C D E Constant Acceleration Constant Velocity At B,C & D there is instantaneous change in acceleration Area Under Graph = Total Distance Travelled Velocity - Time Graphs

33. Dynamics 7 September 2015 Velocity Time 0 0 Acceleration is constantly changing (In this case it is decreasing) Rise Run  A Acceleration AT A = Rise/Run = Gradient of the tangent AT A Velocity - Time Graphs Tangent drawn at A

34. Dynamics 7 September 2015 Velocity Time 0 0 Acceleration is constantly changing (Increasing) Rise Run  A Acceleration AT A = Rise/Run = Gradient of tangent AT A Velocity - Time Graphs

35. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (a) Constant Velocity Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468

36. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (a) Constant Velocity Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468

37. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (a) Constant Velocity Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468 Distance travelled = area under graph = area of rectangle = length x breadth = 8 x 8 = 64m

38. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468

39. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468

40. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468 Distance travelled = area under graph = area of triangle = ½ base x height = ½ 8 x 8 = 32 m

41. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468 Distance travelled= area under graph = area of triangle = ½ base x height = ½ 8 x 8 = 32 m Acceleration= gradient = rise/run = 8/8 = 1 ms -2

42. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (c) Uniform Deceleration Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468

43. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (c) Uniform Deceleration Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468 Distance travelled= area under graph = ½ base x height = ½ 10 x 10 = 50m

44. Dynamics 7 September 2015 Velocity - Time Graphs: Examples (c) Uniform Deceleration Velocity (ms -1 ) Time (s) 10 8 6 4 2 0 0 2468 Distance travelled= area under graph = ½ base x height = ½ 10 x 10 = 50m Acceleration= gradient = rise/run = -10/10 = -1 ms -2 (Deceleration= +1 ms -2

45. Dynamics 7 September 2015 A car starts from rest and accelerates uniformly to 20m/s in 10 seconds. It travels at this velocity for a further 30 seconds before decelerating uniformly to rest in 5 seconds. (a)draw a velocity - time graph of the car’s journey (b)calculate the car’s initial acceleration (c)calculate the car’s final deceleration (d)calculate the total distance travelled by the car (e)calculate the distance travelled by the car in the final 25 seconds Velocity - Time Graphs: Example

46. Dynamics 7 September 2015 Velocity Time 0 0 Velocity - Time Graphs

47. Dynamics 7 September 2015 Velocity Time 0 0 20 (m/s) (s) 104045 Velocity - Time Graphs

48. Dynamics 7 September 2015 Velocity Time 0 0 20 (m/s) (s) 104045 Velocity - Time Graphs

49. Dynamics 7 September 2015 Velocity Time 0 0 20 (m/s) (s) 104045 Velocity - Time Graphs

50. Dynamics 7 September 2015 Velocity Time 0 0 20 (m/s) (s) 104045 Velocity - Time Graphs

51. Dynamics 7 September 2015 Velocity Time 0 0 20 (m/s) (s) 104045 Initial acceleration = initial gradient = rise/run = 20/10 = 2m/s 2 Velocity - Time Graphs

52. Dynamics 7 September 2015 Velocity Time 0 0 20 (m/s) (s) 104045 final acceleration = final gradient = rise/run = -20/5 = -4m/s 2 Velocity - Time Graphs

53. Dynamics 7 September 2015 Velocity Time 0 0 20 (m/s) (s) 104045 A BC Total distance travelled = total area under graph = area A + B + C = ½ x 10 x 20 + 30 x 20 + ½ x 5 x 20 = 100 + 600 + 50 = 750m Velocity - Time Graphs

54. Dynamics 7 September 2015 Velocity Time 0 0 20 (m/s) (s) 104045 C Distance travelled in final 25s = part area under graph = area D + C = 20 x 20 + ½ x 5 x 20 = 400 + 50 = 450m D 20 Velocity - Time Graphs

55. Dynamics 7 September 2015 Velocity-time graphs 80 60 40 20 0 10 20 30 4050 Velocity m/s T/s 1) Upwards line = 2) Horizontal line = 3) Steeper line = 4) Downward line =

56. Dynamics 7 September 2015 80 60 40 20 0 1)How fast was the object going after 10 seconds? 2)What is the acceleration from 20 to 30 seconds? 3)What was the deceleration from 30 to 50s? 4)How far did the object travel altogether? 10 20 30 4050 Velocity m/s T/s