2. Vectors A vector is a quantity that involves both magnitude and direction. – 55 mph north – A downward force of 3 Newtons A scalar is a quantity that does not involve direction. – 55 mph – 18 cm long

3. Vector Notation Vectors are often identified with arrows in graphics and labeled as follows: A Vector A represents motion 10 cm to the right. AA XYZ 

4. Vectors and Direction In drawing a vector as an arrow you must choose a scale. If you walk five meters east, your displacement can be represented by a 5 cm arrow pointing to the east.

5. Suppose you walk 5 meters east, turn, go 8 meters north, then turn and go 3 meters west. Your position is now 8 meters north and 2 meters east of where you started. The diagonal vector that connects the starting position with the final position is called the resultant.

6. The resultant is the sum of two or more vectors added together. You could have walked a shorter distance by going 2 m east and 8 m north, and still ended up in the same place. The resultant shows the most direct line between the starting position and the final position.

7. Vector Addition A B C D E A B C D E A B C D E R A + B + C + D + E = Distance R = Resultant = Displacement RR

10. Calculate a resultant vector An ant walks 2 meters West, 3 meters North, and 6 meters East. What is the displacement of the ant?

11. Displacement Displacement is an object’s change in position. Distance is the total length of space traversed by an object. 5m 3m 1m  mmmm mmm 9135 Distance 7.636ntDisplaceme 22   6.7m Start Finish = 500 m m m 005 Distance 0 Displacement  

12. Finding Vector Components Graphically Draw a displacement vector as an arrow of appropriate length at the specified angle. Mark the angle and use a ruler to draw the arrow.

14. Finding the Magnitude of a Vector When you know the x- and y- components of a vector, and the vectors form a right triangle, you can find the magnitude using the Pythagorean theorem.

15. Forces in Two Dimensions Force is also represented in x-y components.

17. Rectangular Components A B R  Quadrant I Quadrant II Quadrant IIIQuadrant IV y -y x -x