1. PH 201 Dr. Cecilia Vogel Lecture 4

2. REVIEW  Acceleration and graphs  derivatives  Constant acceleration  x vs t, v vs t, v vs x OUTLINE  Vectors  notation  magnitude and direction  components  vector equations

3. Vectors  In one dimension, you can describe a vector by a number & a sign. In 2-D or 3-D that’s not enough.  In 2-D, you need to give _____2____ numbers with signs, in 3-D, need ___3_____  For example, surface of Earth is 2-D, need to give latitude and longitude

4. Vectors in 2-D  Both these vectors are described by (0,0) (4,5) (2,6) (6,11) x-component y-component

5. Length of Vector (0,0) (4,5)

6. Components of Vector If the vector has length A and direction angle q measured counterclockwise from the +x-axis, then A x =Acos(q) = x-component of vector A A y =Asin(q) = y-component of vector A

7. Size and direction of Vector If the vector has x-component A x and y- component A y, then the magnitude of the vector is A=sqrt(A x 2 +A y 2 ) the direction angle is q=tan -1 (A y /A x ) IF the angle is in the first quadrant. If not, you may have to adjust to the correct quadrant (because your calculator can’t tell the diff between -4/3 and 4/-3, for example).