Distances and displacements Distance is ____________________________________ or _________________________________________________ how far an object moves the change in position of an object initial position xi final position xf change in position = xf - xi = Dx Instead of _________ , we will use _____ for distance. We will use SI (international system) units. The SI unit for distance is the ___________ . Any other unit for distance must first be ___________ _______________________ before using any equation in Regents Physics. Dx d meter changed to meters

scalars magnitude ______________– quantities with ______________(size) only Ex: distance d = 2.0 m magnitude vectors ____________– quantities with magnitude and _________ direction direction Ex: displacement d = 2.0 m, west distance = magnitude Distance d is a _______________. Displacement d is a_____________________ . scalar vector. Vectors are represented by ________________: arrows

Ex: Draw d = 2.0 m, west. Use a scale of 1 cm:1 m. Use a scale of 1cm:1 m to draw d. head tail magnitude must have arrow __________ for_________________ use a ___________ to draw a scale and straight line right or up is______________; down or left is ___________ right =___________; up =_______________, etc any vector with same mag. and dir. is_______________ head direction ruler negative positive east north equal Ex: All these vectors are _________________ because they have the same _______________ and _______________: equal magnitude direction

Use a ruler to draw the vectors to the scale: 1 cm:1 m A = 2m, E B = 3m, E Adding vectors  add using the ________________method.  draw the _____________ displacement _____ as an ________ from the ________ of A to the ________ of B “head to tail” resultant R head arrow tail A B Ex: R Resultant R = _________ 5 m, E R = _____________ Total distance traveled = _________ Resultant displacement =____________ A + B mag. dir. 5m. 5m, E

Ex. What is B + A = ? B A R R =__________ The ________________ displacement R = ____________ magnitude of R: _________ direction of R: _________ B + A resultant 5m, E 5m E Notice that this new R is same as _________________  The ______________ in which vectors are added __________________________ . This is true even if you add ______________________________________ . A + B order does not matter more than two vectors.

Ex: If A = 3m, east 3 m, west Then –A = ___________ or = __________ (the __________ sign shows direction) -3 m negative Then -X = If X = Compared to X, -X has the same ________________ , but the opposite _____________________ . magnitude direction

III. Subtracting vectors using the head to tail method. A = 2m B = 3m Given: -B A + (-B) Find A – B = ____________ R A A + (-B): -B 1 m mag. = ______ dir. = ______ R =_________ = _________ 1m, W -1 m W Total distance traveled =___________ but resultant displacement = ______________ 5 m 1 m, W

Ex: Using same vectors, what does B – A = ? B = 3 m A = 2m -A B B + (-A) B – A =_____________ R -A 1 m, E +1 m R = __________ = _________ 5 m. Total distance covered = ______________ Resultant displacement =______________ 1 m, E resultant Notice that the ____________________ here is exactly __________________ to the one in the previous example. opposite

√(32 + 42) IV. Adding non-parallel vectors. C Find C + D 4 m 3 m D R q 4 m √(32 + 42) start here mag. of R = ____________ 5 m =___________ 5 m, 370 N of E R = _________________ Total distance = _______ dir. of R: q = tan-1 (3/4) 7 m = 370

√(32 + 42) Ex: What is D + C? C 4 m D 3 m mag. of R = ____________ R =___________ q dir. of R: q = tan-1 (4/3) = 530 start here 5 m, 530 E of N R =__________________ R could also be written: R = _______________________________________ R = 5 m, 370 N of E (Same as C + D)

IV. Subtracting non-parallel vectors. Ex. Find C – D = C + (–D) D -D C 4 m 3 m 3 m start here 4 m q R 3 m 5 m mag. of R = ____________ dir. of R: q = tan-1 (3/4) 5 m, 370 S of E R = __________________ = 370 Total distance =____________ 7 m.

R = __________________ Ex. Draw D- C. = D + (–C) 4 m C: D -C: 3 m 4 m 4 m mag. of R = ________ 5 m dir. of R: q = tan-1 (4/3) R 3 m = 530 q 5 m, 530 W of N R = __________________ start here Total distance =____________ 7 m.