1. Draw the distance-time graph displacement / m time / s 8 4 2 -2 18 10

2. RECAP total distance / m time / s 8 6 10 4 18 displacement / m time / s 8 4 2 -2 18 10 0 0

3. These are distance-time graph and displacement-time graph The slope of a distance-time graph represents the speed of the object The slope of a displacement-time graph represents the velocity of the object The different gradient / steepness of the slope of a distance-time graph means that the object is moving at a different speed POP-QUIZ These are distance-time graph and displacement-time graph The slope of a distance-time graph represents the speed of the object The slope of a displacement-time graph represents the velocity of the object The different gradient / steepness of the slope of a distance-time graph means that the object is moving at a different speed

4. The steeper the slope of a distance-time graph, the faster the speed of the moving object If the slope of a distance-time graph is of constant steepness, it represents that the object is moving at a constant/uniform speed If the slope of a distance-time graph is horizontal, it represents that the object is stationary If the slope of a distance-time graph is not of constant steepness, i.e. a curving slope, it represents that the object is moving at a non-uniform speed POP-QUIZ The steeper the slope of a distance-time graph, the faster the speed of the moving object If the slope of a distance-time graph is of constant steepness, it represents that the object is moving at a constant/uniform speed If the slope of a distance-time graph is horizontal, it represents that the object is stationary If the slope of a distance-time graph is not of constant steepness, i.e. a curving slope, it represents that the object is moving at a non-uniform speed

5. INTERPRET THE GRAPH total distance / m time / s 0 A B C DE F object is stationary object is travelling at uniform speed object is travelling at non-uniform speed increasing speed decreasing speed ?

6. WHAT IS THE SPEED? total distance / m time / s D 10 5 30 35

7. WHAT IS THE SPEED? total distance / m time / s D 10 5 30 35 1 m/s ? RUN = 5 s RISE = 5 m AVERAGE SPEED = 1 m/s total distance travelled ---------------------------------- total time taken

8. WHAT IS THE SPEED? total distance / m time / s D 10 5 30 35 1 m/s ? AVERAGE SPEED = 1 m/s “SPEED” = 1 m/s ? X X 34 34.5 9 6 RISE = 3 m RUN = 1 s INSTANTANEOUS SPEED = 3 m/s 35 y 2 – y 1 ------------------------ x 2 – x 1

9. Average speed : Instantaneous speed : WHAT IS THE SPEED? “total distance travelled divided by total time taken” “calculating the gradient of the tangent at the point of interest”

10. POP-QUIZ total distance / m time / s 8 6 10 4 18 0 WHAT IS THE ASSUMPTION I MADE FOR SALLY’S JOURNEY? SALLY’S SPEED IS UNIFORM BETWEEN 0-8 / 8-10 / 10-18 s WHAT IS THE AVERAGE SPEED FOR THE JOURNEY? 0.56 m/s WHAT IS THE INSTANTANEOUS SPEED AT POINT G? 1.00 m/s X Point G

11. SPEED–TIME GRAPH Distance-time graph / Displacement-time graph Speed-time graph / Velocity-time graph Acceleration-time graph Distance-time graph / Displacement-time graph Speed-time graph / Velocity-time graph Acceleration-time graph

12. SPEED–TIME GRAPH total distance / m time / s 8 6 4 10 18 10 0 speed / m/s

13. SPEED-TIME GRAPH total distance / m time / s 8 6 4 10 18 10 0 speed / m/s time / s 8 0.5 1.0 18 10 0

14. speed / m/s SPEED-TIME GRAPH total distance / m time / s 8 6 10 4 18 14 2024 0

15. SPEED-TIME GRAPH total distance / m time / s 8 6 10 4 18 14 2024 0 speed / m/s time / s 8 0.5 10 1.0 18 2.0 2024 0

16. total distance / m time / s UNIFORM VS NON-UNIFORM INCREASE 1 s 2 m 4 m 6 m X X X

17. total distance / m time / s UNIFORM VS NON-UNIFORM INCREASE 1 s 2 m 5 m 100 m X X X

18. SPEED-TIME GRAPH time / s 8 6 10 4 18 14 2024 0 total distance / m 18 28 speed / m/s

19. SPEED-TIME GRAPH time / s 8 6 10 4 18 14 2024 0 total distance / m 18 28 time / s 8 10 0.5 1.0 18 2024 0 speed / m/s 2.0 28

20. AREA UNDER SPEED-TIME GRAPH time / s 8 6 10 4 18 14 2024 0 total distance / m 18 28 time / s 8 10 0.5 1.0 18 2024 0 speed / m/s 2.0 28

21. POP-QUIZ speed / m/s 8 0.5 1.0 26 18 time / s 0 total distance / m 8 4.0 14.0 26 18 time / s 0 18.0

22. graphical analysis of motion From the velocity-time graph of a object, we can obtain 3 important pieces of information. 1.Instantaneous velocity (read off y-axis) 2.Acceleration = gradient of the graph = 3.Distance travelled = area under the graph = ½ (u + v) t v – u Δ t time/ s velocity/m s -1 Recall Area of trapezium = ½ x (a + b) x height u v t

23. Solution Acceleration = gradient of v-t graph = = - 6.3 m/s 2 (2sf) graphical analysis of motion The motion of a car is described by the velocity-time graph below. Find i) The acceleration of the car between points A and B The motion of a car is described by the velocity-time graph below. Find i) The acceleration of the car between points A and B –5 – 20 8 – 4 time/s velocity/m s -1 -5 20 4 7 8 11 A B

24. Solution Average speed = = Total Area = Area of X + Area of Y = ½(7)(20) + ½(4+3)(5) = 87.5 m Average speed = 87.5/11 = 8.0 m/s (2sf) graphical analysis of motion The motion of a car is described by the velocity-time graph below. Find ii) The average speed of the car The motion of a car is described by the velocity-time graph below. Find ii) The average speed of the car Total distance Total time time/s velocity/m s -1 -5 20 4 7 8 11 A B Area under graph Total time X Y

25. Solution Displacement of car, s = (+ve dist) – (–ve dist) = Area of X – Area of Y = ½(7)(20) - ½(4+3)(5) = + 52.5 m Or 52.5 m in the positive direction graphical analysis of motion The motion of a car is described by the velocity-time graph below. Find iii) The total displacement of the car The motion of a car is described by the velocity-time graph below. Find iii) The total displacement of the car time/s velocity/m s -1 -5 20 4 7 8 11 A B X Y

26. A toy car moves from point X to point Y at a constant speed of 2 m/s, passing the observer at O. Sketch the displacement-time graph for the motion of the toy car. O X Y Positive direction displacement/m time/s 14 m 8 m 8 –14 x y To find time x (+ve part of graph) Velocity = Gradient of the graph -2= x= 4 To find time y Velocity = Gradient of the graph -2= y= 11 0 - 8 x - 14 - 8 y 4 11

28. Small gradient Small velocity time/s displacement/m Displacement-time graphs The object is experiencing increasing velocity in the positive direction graphical analysis of motion Larger gradient Increasing velocity Gradient is positive throughout Velocity is positive Object moves in positive direction a) What motion is described by the displacement-time graph below?

29. time/ s displacement/ m graphical analysis of motion Displacement-time graphs Large gradient High velocity Smaller gradient Decreasing velocity Gradient is positive throughout Velocity is positive Object moves in positive direction The object is experiencing decreasing velocity in the positive direction b) What motion is described by the displacement-time graph below?

30. time/ s displacement/ m graphical analysis of motion c) What motion is described by the displacement-time graph below? Displacement-time graphs steeper gradient Increasing velocity Small gradient Small velocity Gradient is negative throughout Velocity is negative Object moves in negative direction The object is experiencing increasing velocity in the negative direction

31. time/ s displacement/ m graphical analysis of motion Displacement-time graphs Steep gradient Large velocity gentler gradient Decreasing velocity Gradient is negative throughout Object moves in negative direction Negative gradient does not imply object moving towards observer Displacement approach zero either from +ve or – ve direction implies object moving towards observer The object is experiencing decreasing velocity in the negative direction d) What motion is described by the displacement-time graph below?

32. Deceleration vs Acceleration Let's suppose we define East as positive. Consider each of the following situations with this sign convention for all. Suppose we have a car traveling West and speeding up. 1. Is velocity negative or positive? Answer: negative 2. Is acceleration negative or positive? Answer: negative Suppose we have a car traveling West and slowing down. 1. Is velocity negative or positive? Answer: negative 2. Is acceleration negative or positive? Answer: positive Suppose we have a car traveling East and speeding up. 1. Is velocity negative or positive? Answer: positive 2. Is acceleration negative or positive? Answer: positive Suppose we have a car traveling East and slowing down. 1. Is velocity negative or positive? Answer: positive 2. Is acceleration negative or positive? Answer: negative