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Distance and displacements

Distance and displacements. Causeway Bay. Wan Chai. Simon is in Causeway Bay . He needs to. 1 take a book to Mary at the exit gate of Mongkok MTR , and. 2 pass a gift to Jenny at the HKEAA in Wan Chai . Mongkok. From. To. Adult Fare. Causeway Bay. Mongkok. $10.0. Mongkok.

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Distance and displacements

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  1. Distance and displacements

  2. Causeway Bay Wan Chai Simon is in Causeway Bay. He needs to 1 take a bookto Mary at the exit gate ofMongkok MTR, and 2 pass a gift to Jenny atthe HKEAA in WanChai. Mongkok

  3. From To Adult Fare Causeway Bay Mongkok $10.0 Mongkok Wan Chai $10.0 Causeway Bay Wan Chai $3.8 (a) What is the minimum fare for Simon’s whole journey? Hedoesn’t goout of the gates at Mongkok station.

  4. From To Adult Fare Causeway Bay Mongkok $10.0 Mongkok Wan Chai $10.0 Causeway Bay Wan Chai $3.8 Warm-up (a) What is the minimum fare for Simon’s whole journey? For his whole journey, hisposition changes from CausewayBay station to Wan Chai station.

  5. (b) Do you agree with the following statements about travelling by MTR? Disgree Agree More should be paid for longer distance travelled.  Fare depends on where he passesthe exit gate only. 

  6. X North Pole Y 1 Unit of length Symbol:m SI unit: metre Old definition: 1 m was defined as 10–7 of a quadrant of the Earth. But no need to remember the exact value…

  7. 2 Displacement and distance Displacement requires : • Lengthof a straight line going fromthe old to the new positions i.e. size/magnitude • Direction of the movement Simulation

  8. 2 Displacement and distance your home To go to school from home... Size = length of this arrow your school displacement from home to school A displacement has size & direction.

  9. 2 Displacement and distance your home To go to school from home... l1 l2 l3 your school Distance = length of pathyou travelled = l1 + l2 + l3 ( size of displacement)

  10. 3 Vectors and scalars Vector a quantity described by its direction &magnitude (size) E.g.displacement, velocity, force

  11. 3 Vectors and scalars A vector can be represented by an arrow. It tells us: direction length = magnitude

  12. 3 Vectors and scalars To go from A to B... path taken start point end point   A B displacement displacement written as AB

  13. 3 Vectors and scalars Scalar • quantity described by its magnitude (size) only E.g. temperature, distance, speed, mass, energy

  14. N 3 km 7 km north 4 km 4 Adding displacements a Graphical method A car travels 4 km north then 3 km north. total distance total distance = ? = (3 + 4) km = 7 km total displacement = ? total displacement = (3 + 4) kmnorth = 7 kmnorth

  15. N 1 km north 3 km 4 km 4 Adding displacements a Graphical method A car travels 4 km north then 3 km south. total distance total distance = ? = (3 + 4) km = 7 km total displacement = ? total displacement = (3 + 4) kmnorth = 1 kmnorth

  16. N 3 km  4 km 4 Adding displacements a Graphical method A car travels 4 km north then 3 km east. total distance = ? total distance = (3 + 4) km = 7 km total displacement = ? total displacement 5 km = 5 km37 east of north (by measurement)

  17. ‘tip’ of p joined to ‘tail’ of q p q p + q 4 Adding displacement Tip-to-tail method: a Graphical method

  18. 3 tan  = 4 3 km  4 km 4 Adding displacements b Algebraic method It is easy to adddisplacements if they are perpendicular to each other. E.g. d 2 = 42 + 32 d = 5 km N d 5 km  = 37

  19. 70 m Example 2 A girl cycles a circulartrack of diameter 70 m and stops atthe starting point. (a)Distance travelled = ? Distance travelled = perimeter of track = p× 70 = 220 m

  20. 70 m Example 2 (b) Does she change her position? No, it is because she goes back to the starting position.

  21. 4km 5km Example 3 A car travels 5 km north and 4 km east. (a) Total distance travelled = ? N Total distance = 5 + 4 = 9km

  22. 70 m Example 2 (c) What is her displacement? Her overall displacement = 0 m

  23. 4km 5km Example 3 A car travels 5 km north and 4 km east. (b) What is the displacement? N size = = 6.40 km tan  =   = 38.7 6.4km  Total displacement: 6.40 km 38.7° east of north

  24. Q1 A ball suspended... A ball hung by a string swings from X to Y. What is the size of the displacement ofthe ball? 60o 1 m A p/3 m B 1 m C 1 m towardsthe right 1 m X Y

  25. Q2 Is the speed limit... Is the speed limit a vector or a scalar? Scalar!

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