Notes- Distance and Displacement

Distance and Displacement

Defintion of Scalar and Vector- these words will be important in that they help describe value (think math).
Scalar: quantities which are fully described by a magnitude (or numerical value) alone.
Vector: quantities which are fully described by both a magnitude and a direction.

Here are some example for you to categorize as either scalar or vector. Highlight the box to see the correct answer.

Quantity	Category
5 m	scalar
30 m/sec, East	vector
5 mi., North	vector
20 degrees Celsius	scalar
256 bytes	scalar
4000 Calories	scalar

Let's look at distance and displacement

    Distance: scalar quantity
            which refers to "how much ground an object has covered" during its motion.
Displacement: vector quantity
            which refers to "how far out of place an object is"; it is the object's overall change in position.

Look at the diagram below

                1. If I walked 4 meters east and then 2 meters south, contining 4 meters west and finished my walk after another 2 meters north
                    What distance did I cover?
                            You would add the total distance I covered.
                                    4meters + 2 meters + 4 meters + 2 meters.
                                            I covered a total of 12 meters.

                        However if I ask what was my displacement. I would not say the same amount.
                              I actually have 0 meters in displacement because I am back to where I started

2. Let take another look at the diagram and do another measurement reading

                    If I walked 4 meters east and then 2 meters south so I could eat at the restaurant. I traveled a total distance of 6 meters.
                    If I wanted to express my displacement I would draw a line from where I started to where I ended up.
Draw a line from the top left corner to the bottom right corner. Do you remember what to do with a right triangle to figure the unknown side? a² + b² = c² Then find the square root of c²
(4m X 4m = 16m²)   + (2m X 2m = 4m²) = 20m² (find the square root) ~4.5 meters

We can express my displacement as being approximately 4.5 meters southeast.
magnitude direction

The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.

Use the diagram to determine the resulting displacement and the distance traveled by the skier during these three minutes.

Highlight the space after the statement to see the answer The skier covers a distance of _80 m + 140 m + 100 m) = 420 m (1 The skier has a displacement of_ 140 m, rightward.