1 of 9 © Boardworks Ltd 2009 2 of 9 © Boardworks Ltd 2009 What is a scalar? Scalar quantities are measured with numbers and units. length temperature time (e.g. 16 cm) (e.g. 102 °C) (e.g. 7 s) 3 of 9 © Boardworks Ltd 2009 What is a vector? Vector quantities are measured with numbers and units, but also have a specific direction. acceleration displacement force (e.g. 30 m/s2 upwards) (e.g. 200 miles northwest) (e.g. 2 N downwards) 4 of 9 © Boardworks Ltd 2009 5 of 9 © Boardworks Ltd 2009 6 of 9 © Boardworks Ltd 2009 7 of 9 © Boardworks Ltd 2009 8 of 9 © Boardworks Ltd 2009 Displacement Displacement is the change in position of an object and is a ______ vector quantity. Distance traveled is a _____ scalar quantity. 9 of 9 © Boardworks Ltd 2009 Dot Diagrams In this dot diagram, each position of the velociraptor is represented as a single point. The time interval between successive dots is constant. Object is speeding up. 10 of 9 Object is slowing down. © Boardworks Ltd 2009 11 of 9 © Boardworks Ltd 2009 12 of 9 © Boardworks Ltd 2009 13 of 9 © Boardworks Ltd 2009 14 of 9 © Boardworks Ltd 2009 15 of 9 © Boardworks Ltd 2009 16 of 9 © Boardworks Ltd 2009 17 of 9 © Boardworks Ltd 2009 18 of 9 © Boardworks Ltd 2009 19 of 9 © Boardworks Ltd 2009 20 of 9 © Boardworks Ltd 2009 21 of 9 © Boardworks Ltd 2009 22 of 9 © Boardworks Ltd 2009 23 of 9 © Boardworks Ltd 2009 24 of 9 © Boardworks Ltd 2009 25 of 9 © Boardworks Ltd 2009 26 of 9 © Boardworks Ltd 2009 27 of 9 © Boardworks Ltd 2009 28 of 9 © Boardworks Ltd 2009 29 of 9 © Boardworks Ltd 2009 Speed or velocity? Distance is a scalar and displacement is a vector. Similarly, speed is a scalar and velocity is a vector. Speed is the rate of change of distance in the direction of travel. Speedometers in cars measure speed. Velocity is a rate of change of displacement and has both magnitude and direction. Averages of both can be useful: average speed 30 of 9 = distance time average displacement = velocity time © Boardworks Ltd 2009 31 of 9 © Boardworks Ltd 2009 32 of 9 © Boardworks Ltd 2009 33 of 9 © Boardworks Ltd 2009 Adding vectors Displacement is a quantity that is independent of the route taken between start and end points. If a car moves from A to B and then to C, its total displacement will be the same as if it had just moved in a straight line from A to C. C B Two or more displacement vectors can be added “nose to tail” to calculate a A resultant vector. resultant vector Any two vectors of the same type can be added in this way to find a resultant. 34 of 9 © Boardworks Ltd 2009 Simplifying vectors Because of the way vectors are added, it is always possible to simplify a vector by splitting it into components. Its displacement is the same, but it is now much easier to describe. How would you describe the car’s displacement in component terms? C B y A x x component D The car has a final displacement of x miles east and y miles north. This can be represented by (x,y). 35 of 9 © Boardworks Ltd 2009 y component Imagine that instead of traveling via B, the car travels via D: Understanding vector calculations 36 of 9 © Boardworks Ltd 2009
