Motion Goal 2

Motion The change in position Two types 1. Scalar Quantities: no direction is indicated Example: the dog walked 5 meters 2. Vector Quantities: direction is indicated Example: the dog walked 5 meters east Directions: North, East, South, West

Distance and Displacement Distance: how far (in meters) an object travels Displacement: the change in position of an object.

Displacement Along a Straight Line You can calculate displacement using the formula: ∆d=df-di ∆d=displacement df= final position di= initial position

Calculating Displacement To determine displacement, draw a number line. If you move to the right, your displacement is positive or east If you move to the left, your displacement is negative or west.

Calculating Displacement Ex. di= 3 df= 7 So, the change or ∆ in d= 4 because 7-3=4

Examples Ex. di= -2 df= 7 What’s ∆d??

Distance vs. Displacement Distance: a scalar quantity Displacement: a vector quantity A straight line that connects the origin and the final destination You must indicate the direction of the displacement Origin (O) 5 Meters Final (F) 7 Meters Southeast (SE)

Calculating Displacement in Different Directions Calculate the total distance by adding all given distances. Draw the diagram on graph paper using the scale: 1unit = 1 square Draw in displacement arrow (from beginning of 1st arrow to the end of the last arrow) Use Pythagorean Theorem to solve for displacement.

Distance vs. Displacement Origin (O) 5 Meters Final (F) 7 Meters Southeast (SE)

How to Use Pythagorean Two different situations: 1. If you have a right triangle (2 arrows total): A2+B2=C2 A= Distance of 1st vector (arrow) B= Distance of 2nd arrow C= Final distance of displacement arrow

Distance vs. Displacement Right triangle Origin (O) 5 Meters Final (F) 7 Meters Southeast (SE)

How to Use Pythagorean Next, solve for C. To do this, you have to plug your numbers into the equation (A2+B2=C2 ) A=5 B=5 C2=? 52 + 52 = C2 25+25= C2

How to Use Pythagorean To get rid of the square in C2 , you must take the square root of both sides! √25+25=√C √50= 7.07m So, the final displacement is 7m, SE

Distance vs. Displacement Right triangle Origin (O) 5 Meters Final (F) 7 Meters Southeast (SE)

How to Use Pythagorean 2nd situation is when you have more than 2 arrows. For example: You walk 5 meters north. You then walk 3 meters east. Next, you walk 2 meters south. Calculate distance the same way as well as draw it out on the graph and draw in your displacement arrow.

How to Use Pythagorean You will not have a right triangle, so you must make one with the lines you have drawn. 3 Meters 2 Meters 5 Meters

How to Use Pythagorean Now that you have a right triangle, you must determine the length of the sides. The top is 3 m since it is the same length as the other top line. The left side was originally 5m, but now you need to subtract 2, so it is 3 m long.

How to Use Pythagorean Next, plug values into the equation: A2+B2=C2 A=3m B=3m C2=? 32 + 32 = C2 9+9=C2 √18=√C ANS= 4.24 meters, SW