1. R ELATIONSHIPS BETWEEN SCALAR AND VECTOR MEASUREMENTS Speed, distance, velocity, displacement, and time

2. W HAT IS A S CALAR Q UANTITY ? Scalar quantities are a measurement only of magnitude or size An example of this would be speed 60 km/h 20 m/s Other examples of scalar measurements would be Length, area, volume, and mass Notice that none of these has a direction associated with it

3. W HAT IS A V ECTOR QUANTITY ? Vector quantities have both a magnitude, or size as well as a direction. A speed such as 23 m/s is just a scalar quantity, but when a direction is added it becomes a vector quantity. 23 m/s travelling north is a vector quantity, it is denoted 23 m/s [N]. This measurement is called velocity, not to be confused with speed! Other examples of vector quantities are position, acceleration and momentum

4. D ISTANCE AND D ISPLACEMENT : Distance (d) is a measure of the length travelled on a path, if there is no direction placed on the distance it is a scalar quantity and is calculated by adding the distances travelled Δd = d 1 + d 2 Displacement ( Δd) is the change in position due to movement The equation for finding displacement is Δd = d f – d i the delta (Δ) means “change in” so for the equation Δd = d 1 + d 2, change in distance = distance 1 plus distance 2 You can see that vector quantities have an arrow above their symbols, this tells you that there is a direction associated with the measurement which means that it is a vector.

5. D ISTANCE AND D ISPLACEMENT So if a person walks to the shoe store west, then turns around and walks east to the food court, what is the distance travelled and the displacement ? - 10m 0m 40m Distance: Δd=d 1 +d 2 so: 10m +50m = 10m then Displacement: Δ d= d f - d i so 0m+ 40m = 40m [E]

6. S AMPLE : On the football field, the Giants have the ball at the 20 yard line. The Giants move the ball 30m down the field, then loose the ball and the opposing team advances the ball 20m back up the field. What is the displacement of the line of scrimmage from the starting scrimmage line Δ d? What distance has the scrimmage line travelled Δd? 30m 20m

7. A N E XAMPLE 1 Vounteer Count your steps! We will assume that you are taking 1m steps Start at the front of the class, and travel 10 steps towards the back of the class Now travel 6 steps back towards the front What distance have they travelled? What is their displacement?