1. 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

2. 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

3. 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

4. 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

5. 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.

6. 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

7. 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

8. 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

9. √(32 + 42) IV. Adding non-parallel vectors. C Find C + D 4 m 3 m D Rq
4 m
√( )
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

10. √(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)

11. 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.

12. 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.