Linear Motion Notes (1-dimension kinematics)
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Linear Motion: the way something moves in a straight line
3 variables to consider:
o Distance/displacement
o Velocity
o Acceleration
Displacement: a vector quantity with a direction
Distance: length between 2 things
Velocity: speed in a given direction (vector quantity)
Rate: a quantity divided by a time interval
o Mi/hr
o m/s
o ft/min
Speed: a measure of how fast something is moving
Instantaneous speed = speed at specific velocity or speed
V

=
Acceleration (speeding up): a change of velocity or speed (
a=
=
vector quantity)
Graphing Etiquette
1. TITLE!!
a. All graphs should have a title that describes the relationship being analyzed
2. LABEL AXES
a. Both X and Y axes need to be properly labeled
i. Include the proper variable and the units represented on the graph
b. Independent variable goes on the X-axis
i. The independent variable is the variable that is changed by the
experimenter
ii. There should only be one independent variable in every experiment
iii. Time will be the independent variable in many experiments
c. Dependent variable goes on the Y-axis
i. The dependent variable ‘depends’ on or is caused by the change of the
independent variable
3. FILL THE ENTIRE GRID OR PAGE
a. Scale the graduations (a.k.a. tic marks) on the axes appropriately in order to make
use of the entire space provided to better display your graph
4. LINE OF “BEST FIT”
a. It is NOT simply connecting the dots
b. Line of best fit (or trend line) is a line drawn through the data points that best
represents the overall trend of the data
i. Linear relationships are the most often, but do not limit your results
ii. Be as accurate as possible
Linear Motion Graphs
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Position (distance - x) vs. time
x
Not moving
(standing still) or
(stationary)
t
x
moving object
constant rate of speed
t
x
moving object
changing velocity
acceleration
t
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Velocity ( v ) vs. time
v
Constant velocity
No acceleration
t
v
Increasing velocity
constant acceleration
t
v
Increasing velocity
Increasing acceleration
t
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Acceleration ( a ) vs. time
a
Constant acceleration
t
Graphing Relationships
Velocity (m/s)
Slope
50
40
30
20
Area under
curve
10
0
Area Under Curve
1
2 3 4 5 6 7
Time (s)
Slope =
Ex:
=
= 6.66 m/s2 = a
Area = ½ bh
Ex: ½(6s)(40m/s) = 3s(40m/s) = 120 m = x
Linear Motion (1-D motion) Equations
Distance (position) = x
Velocity = v
Acceleration = a
Equations to know:
Average velocity
<v> =
=
Average velocity =
Instantaneous Velocity ( and constant acceleration)
1. Vf = Vi + at
2. Vf2 = Vi2 + 2ax
3. X = Vit + ½ at2
[m/s] = [m/s] + [m/s2][s]
[m/s]2 = [m/s]2 + [m/s2][m]
[m/s] = [m/s] + [m/s]
[m2/s2] = [m2/s2] + [m2/s2]
Simplify Equations when Vi = 0
1. Vf = at
2. Vf2 = 2ax
3. X = ½ at2
Simplify Equations when a = 0
1. Vf = Vi
2. Vf2 = Vi2
3. X = Vit
Free Falling Objects
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Any object falling near the surface of the earth free of any contact
A = -9.8 m/s2
Steps to solving problems:
1. State what is given (given variables)
2. State what you are looking for
3.
4.
5.
6.
Select the proper equation to use
Substitute the given variables into the equation
Solve
Sense does this answer make sense?
What goes up, must come down
Position
Speed Max/Min
1
Direction of
Motion
Velocity
Acceleration
Max
Max
9.8 m/s2
2
0
0
3
Max
Max
Projectile Motion (2- Dimensional)
0 m/s
Linear Motion: (vertical)
The speed that the object loses
on the way up, it gains on the
way down
10 m/s
30 m/s
50 m/s
10 m/s
30 m/s
50 m/s
Projectile Motion: (vertical and horizontal)
30 m/s
10 m/s
0 m/s
Parabola (quadratic)
10 m/s
10 m/s
10 m/s
50 m/s
30 m/s
10 m/s
50 m/s
Vertical velocity changes because of gravity, whereas horizontal velocity remains
constant
75°
60°
45°
30°
15°
°
Any angle will travel exactly the same distance as its complimentary angle
Vi = 30 m/s
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25 m
x
Horizontal:
Vi = 30 m/s (constant  no a)
X = Vit + ½ at2
X = Vit
X = 30 m/s (2.26 s)
X = 67.8 m
Vertical:
X = Vit + ½ at2
-25m = 0 + ½ (-9.8 m/s2)(t2)
t2 = 5.102 s2
t = 2.26 s