1 4.2 Distance and displacement Chapter 4 Distance and displacements Unit of length Displacement Vectors and scalars Adding displacements

2 4.2 Distance and displacement SI unit: metre Symbol: m North Pole X Y 1Unit of length 1 m was defined as 10 –7 of a quadrant of the Earth. Old definition: But no need to remember the exact value… But no need to remember the exact value…

3 4.2 Distance and displacement –Length of a straight line going from the old to the new positions –Direction of the movement 2Displacement and distance Displacement requires : i.e. size/magnitude Simulation

4 4.2 Distance and displacement your home your school A displacement has Size = length of this arrow displacement from home to school 2Displacement and distance To go to school from home... size & direction.

5 4.2 Distance and displacement Distance = length of path you travelled (  size of displacement) l1l1 l2l2 l3l3 2Displacement and distance To go to school from home... your home your school = l 1 + l 2 + l 3

6 4.2 Distance and displacement Vector –a quantity described by its E.g. displacement, 3Vectors and scalars & magnitude (size) direction velocity, force

7 4.2 Distance and displacement A vector can be represented by an arrow. It tells us: length = magnitude direction 3Vectors and scalars

8 4.2 Distance and displacement displacement written as AB start point end point A B  3Vectors and scalars  To go from A to B... path taken displacement

9 4.2 Distance and displacement –quantity described by its magnitude (size) only 3Vectors and scalars Scalar E.g. temperature, mass, energy distance, speed,

Distance and displacement total distance = ? total displacement = ? = (3 + 4) km = 7 km total distance total displacement = (3 + 4) km north = 7 km north N 4 km 7 km north 3 km 4Adding displacements aGraphical method A car travels 4 km north then 3 km north.

Distance and displacement 4Adding displacements A car travels 4 km north then 3 km south. 4 km 1 km north 3 km total distance = ? total displacement = ? = (3 + 4) km = 7 km total distance total displacement = (  3 + 4) km north = 1 km north N aGraphical method

Distance and displacement 4Adding displacements A car travels 4 km north then 3 km east. 4 km 3 km  5 km total distance = ? total displacement = ? = (3 + 4) km = 7 km total distance total displacement = 5 km 37  east of north (by measurement) N aGraphical method

Distance and displacement ‘tip’ of p joined to ‘tail’ of q p q p + q Tip-to-tail method: 4Adding displacement aGraphical method

Distance and displacement d 5 km 4Adding displacements bAlgebraic method E It is easy to add displacements if they are perpendicular to each other. E.g. N 4 km 3 km  d 2 =  d = 5 km  = 37  tan  = 3 4

Distance and displacement 60 o 1 m Y Q1A ball suspended... A ball hung by a string swings from X to Y. 1 m X Y What is the size of the displacement of the ball? A  /3 m B1 m C1 m towards the right

Distance and displacement Q2Is the speed limit... Is the speed limit a vector or a scalar? Scalar!

Distance and displacement A girl cycles a circular track of diameter 70 m (a) Distance travelled = ? Distance travelled = perimeter of track =  × 70 = 220 m Example 2 Position, distance and displacement and stops at the starting point. 70 m

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

Distance and displacement (c)What is her displacement? Her overall displacement = 0 m Example 2 Position, distance and displacement 70 m

Distance and displacement E Distance and displacement A car travels 5 km northand 4 km east. (a)Total distance travelled = ? Total distance = = 9 km 5 km 4 km Example 3 N

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