1. Scalars and Vectors With forces direction is important so force is a vector quantity. Time has no direction so it is a scalar quantity.

2. Scalar – magnitude (size) only eg distance, d = 34 km Vector – magnitudeeg. Displacement, s = 34 km - directionsouth - reference point of Edinburgh

3. quantitysymbolunitsymbolScalar vector dmetres Displacementsmetremv Speedv Metres per second m/s or ms -1 s Velocityv Metres per second m/s or ms -1 v Acceleration Metres per second per sec or Time Fnewtons EnergyJ mkilogramkg

4. quantitysymbolunitsymbolScalar vector Distancedmetrems Displacementsmetremv Speedv Metres per second m/s or ms -1 s Velocityv Metres per second m/s or ms -1 v Accelerationa Metres per second per sec m/s 2 or ms -2 v Timetsecondss ForceFnewtonsNv EnergyEjoulesJs Massmkilogramkgs

5. Directions Left/right, up/down30 o above horizontalNorth, south etc 3 figure bearings 315 o north west

6. Example Draw a scale diagram to find the distance travelled and the final displacement of someone following this route. 4 km at 045 o 2 km due south 6 km at 60 o south of east N resultant Distance = 12 km Displacement = 7.4 km at 128 o Scale 1cm: 1km Now do the extra example sheet

7. (a) If a boy took 4 hours to complete this course, what was his average speed in km/hour? (b) What was his average velocity? (c) What was his velocity in m/s? Distance = 12 km Displacement = 7.4 km at 128 o Average speed = d ÷ t = 12 ÷ 4 = 3 km/h ( b) average velocity = s ÷ t = 7.4 ÷ 4 = 1.85 km/hAt 128 o (c) 1.85 km/h = 1850 m/h = 30.83 m/min = 0.51 m/s at 128 o Now do tutorial questions 14, 15

8. 2010 Higher paper Qu 21 A helicopter is flying at a constant height above the ground. (a)The helicopter flies 20km on a bearing of 180 o (due south). It then turns on to a bearing of 140 o and travels a further 30km. The helicopter takes 15 minutes to travel the 50km. (i)By scale diagram or otherwise find the resultant displacement of the helicopter.(2) (ii)Calculate the average velocity of the helicopter during the 15 minutes.(2)

9. Examples: Find the resultant vector (add vectors nose to tail.) 65 N140 N (a) For forces the resultant vector is called the unbalanced force. (b) 30 o 10 N Now do tutorial questions 16 to 22 ( you might need a hint with Qu 19)

10. 60 o 100 N Example: Resolve the forces on this garden roller to find the horizontal force on it. Now try tutorial questions 23 to 26

11. Tutorial Questions 14 to 26 SAQ 1 to 16 Homework 3 Purple book 1.1 except Qu 2,3 Scalars and Vector Review Make sure you complete all the following.