2. Speed

3. What is speed? Speed is a measure of how fast you are going. It is measured in metres per second (m/s or ms -1 ) It can also be measured in kilometres per hour (km/h or kmh -1 )

4. Speed-Distance-Time To calculate your speed you need to know the distance travelled and the time taken to travel it. Formula:Speed (v) = Distance (s) / Time (t) Units: m/s m s v = s / t Take careful note of the symbols…don’t get mixed up!

5. Speed Examples The world 100m sprint record is held by Usain Bolt in a time of 9.58s. What speed was he running? s=100m t=9.58s v=? v= s / t =100/9.58=10.44m/s

6. Calculating Speed Name Distance (m) Time (s) Speed (m/s)

7. Changing the formula around How to use the triangle: 1.Cover the quantity you want to find. 2. If the two symbols left are beside each other multiply them together. 3. If they are one on top of each other divide the top symbol by the bottom. s tv Can you write down all three equations?

8. Check your answers! Speed = distance / time or v = s / t Time = distance / speed or t = s / v Distance = speed x time or s = vt

9. Using the Motion Sensor Use the Motion sensor to investigate graphing motion.

10. Distance v Time Graphs The graph shows your position as time passes. Questions : 1.What were you doing if the graph was flat? 2.What were you doing if the graph rose to the right? 3.What were you doing if the graph fell to the right? 4.What did the steepness of these slopes tell you?

11. Copy and say what is happening in each graph: Distance v Time Graphs distance (m) t (s) distance (m) t (s) distance (m) t (s) distance (m) t (s) Now answer Q1-7 on p10.

12. Speed on distance time graphs The speed of the object can be seen on a distance time graph as how steep the graph is: fast movement = steep graph slow movement = less steep graph Distance (m) Time (s)

13. Calculating speed from a distance-time graph As we know, speed = distance / time We can do this directly from the graph… For a section of the graph, read off the distance moved, and the time and put into the equation. Distance (m) Time (s) 0 1 2 3 4 5 6 7 8 The distance moved, s is 5m The time, t is 7s v = s / t v = 5 / 7 = 0.7 m/s

14. Distance (m) Time (s) 0 1 2 3 4 5 6 Calculating speed from a distance-time graph What about the following graph? Work out what happened to the distance: It went from 5m to 1m, so s = -4m The time: It went from 1s to 5s, so t = 4s v = s / t, sov = -4 / 4 v = -1 m/s Now answer Q1 on the worksheet ‘Speed and Graphs’.

15. Speed-Time Graphs If this is a distance-time graph: What is a speed time graph? Distance (m) Time (s) Speed Time (s) (m/s)

16. Speed time graphs Not moving: What is our speed if we are not moving? v = 0 m/s, And graph it: A speed time graph of staying still is a straight line at v = 0 m/s Time (s) Speed (m/s) 0 1 2 3 4 0 0 0 0 0 so lets draw a table of this: Speed Time (s) (m/s)

17. Moving at a constant speed: Let us say our speed, v = 1 m/s: so graph it: A speed time graph of moving at a constant speed is a straight line at v. Time (s) Speed (m/s) 0 1 2 3 4 1 1 1 1 1 Speed Time (s) (m/s) Speed time graphs 1

18. Speed-Time graphs Imagine a smart car at a red traffic light: What happens when the light goes green? The car accelerates. What happens to the speed of the car? Draw a speed-time graph of this motion. Time (s) Speed (m/s) 0 1 2 3 4

19. Speed-Time graphs What would this graph look like for a Ferrari? Draw this line on the same graph (don’t worry if it goes off the scale!) What is the difference between the lines? The steeper the graph the faster the acceleration. Time (s) Speed (m/s) 0 1 2 3 4 0 2 4 6 8

20. What is acceleration? Acceleration (a) is how fast are you getting faster. Or your rate of change of speed. Eg. For the smart car. How much did the speed increase each second? 1 m/s every second, or 1 m/s/s We write this a = 1 m/s 2 What was the acceleration of the Ferrari? a = 2m/s 2

21. Acceleration acceleration = change in speed time taken a = v – u t where v = final speed u = initial (start) speed Deceleration is slowing down (negative acceleration).

22. Writing Speed and Acceleration Speed = m/s or ms -1 Acceleration = m/s 2 or ms -2

23. Questions Worksheet ‘Speed & Graphs’ Qs 2-4 p11 Qs 10-15

24. Speed v Time Graphs The area under the Speed v Time graph is equal to the distance travelled. Q:What is the distance travelled by the object in the above graph? A: ½ x (5x10)+ (10x10) + ½ x (10x10) = 25 + 100 + 50 = 175m From our speed formula, what is the equation for distance, s? s = v x t

25. Speed v Time Graphs What is the distance travelled in the following graphs? t (s) speed (m/s) 0 1 1 2 speed (km/s) t (s) t (mins) t (s) 0 0 0 0 0 5 1020 1 2 2468 1234 2 12 1 2 5 10 5 1520 2m 50m 4m 150m 100m 10,000m 1 2 34 56

26. Acceleration With your partner, read out loud and help each other to understand the left hand side of your worksheet (Speed-Time Graphs – Tutorial). Then, answer the Qs on the RHS. (Answer sheet on the front desk to check your answers) Go onto moodle and watch the 2 acceleration videos.

27. Interpreting Graphs Look at the sample graphs - each shows a different type of motion. Moving at a constant velocity. Moving with constant acceleration -velocity increasing at a steady rate from rest (0) example: car accelerating from 0 to 100km/h - typical car test trial

28. Can you describe the motion in the following graphs?

29. Graph Answers Moving with constant acceleration - velocity increasing at a steady rate from an initial velocity Examplecar accelerating from 40 to 60 mph to overtake Example: car accelerating from 40 to 60 mph to overtake

30. Graph Answers Acceleration increasing - velocity increasing at an increasing rateAcceleration increasing - velocity increasing at an increasing rate Example: rocket accelerating away from lift off - constant thrust but burning fuel means that rocket weighs less - so accelerates at a greater rate

31. Graph Answers Moving with constant negative acceleration - velocity decreasing at a steady rate Example: car braking from 60 mph to Zero

32. Graph Answers Car accelerates from rest, travels with a constant velocity, accelerates to overtake then drops back to the steady velocity before braking to a halt.