KINEMATICS
KONICHEK
• I. Position and distance
• A. Position- The separation between an object and a
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reference point
1. To locate something we must make some point a
zero point- reference point
2. Measures both distance and direction
B. Distance- needs no reference.
1. Measures the amount of separation
2. Measurement of only length
C. Time- this is the interval between on reading of
separation to the next reading of separation
D. Speed( rate)= displacement/ time
1. Units of distance/ unit of time
2. Instantaneous speed- the
speed of the object at the time of the
observation.
a. Looking at ones
speedometer.
3. Average speed= total
distance/total time
a.SA= DT/TT
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E. Scalar and vector quantities.
1. Scalar-measures only the magnitude or
size
a. Distance
b. Speed is a scalar- tells only how fast
2. Vector- measures magnitude and
direction
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Velocity
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A. Velocity- Speed in a given direction…
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1.vector
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B. Constant velocity►
1. Motion remains constant at the same
speed
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C. Changing velocity- constant velocity and constant
speed are not the same
1. Constant speed can happen even if direction is
changing
2. Constant velocity cannot occur- changing
direction
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D. Instantaneous velocity- this is the position of a
moving object
1. The position of the object changes with each
new time taken.
 E. Displacement-The change of position
of an object.
 1. Final distance - initial distance= ΔD
 F. Time for moving objects
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1. Final time - initial time=ΔT
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D. Average velocity is the ratio of the
change in displacement to a change in
time
1. Va= d2-d1/t2-t1
E. Constant velocity- Occurs when the
average velocity is the same for all time
intervals
1. Also called uniform velocity:
Δd/Δ t is constant.
a. The equation then comes to
v=d/t. This represents uniform velocity.
F. Position-time graphs.
1. Shows the position as a function of
time
1. Time on X-axis, position on Xaxis
2. Slope of a position- time graph.
a. The ratio of displacement to time
is the same as rise over run of the line
(slope)
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III. POSITIVE AND NEGATIVE
VELOCITIES.
A. Displacement can occur either positive or
negative
1. Positive moves to the right of the
reference point
2. Negative- moves to the left of the
reference point
• B. Time is always positive
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C. Speed is the magnitude of the
velocity
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D. Velocity- includes speed and
direction of a moving object
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1. Can have a positive or negative
velocity
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a. Depends which way the
object is moving relative to the frame of
reference.
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IV. Instantaneous velocity- The finding of the
velocity for an instant.
A. Like looking at the speedometer of your car
for just an instant.
B. It’s the slope of the tangent- If the graph
shows an increasing velocity over various times the
line is not a straight line, so the slope gives the
instantaneous velocity.
1. First derivative of the displacement
formula or limit ΔX/ΔT
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V. Velocity-Time graph- very useful
tool to describe motion.
A. time- x-axis, velocity on the yaxis
B. The area under the line is equal
to the displacement of the object from
its original position
1. When velocity is constant
displacement increases linearly with
time
VI Motion
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A. Speed- How fast an object is moving relative to a reference frame
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1. ratio between distance and time ( scalar quantity-tells how
fast)
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a. speed=distance/time( S=d/t)
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b. m/s, Km/hr, Mi/hr
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2. constant speed- when an equal distance is covered over an
equal time
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3, Graphing speed
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a. time is on X axis
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b. distance on the Y axis
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c. the speed of the car can be calculated by calculating the
slope of the line( rise/ run).. Y=mx+b
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1, steeper the slope faster it’s going
Graphing of Velocity
• Low velocity
High velocity
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VII. Relative velocity- this is the
velocity as seen from a stationary
frame of reference
A. A boat is traveling at 8m/s
and a man on the boat is walking at
2m/s a man observing from the
shore would see the man walking at
10m/s
I. Acceleration- vector quantity
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A. The rate which an objects velocity
changes
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1. Has to do with changing how fast
is moving.
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2. Acceleration occurs when an
object changes its velocity with respect to
time.
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B. Constant velocity-When an object changes its velocity by the
same amount each second.
1. Not the same as a constant velocity
2. The velocity is changing the same amount for every
increment of time
a. constant velocity is not accelerating
3. Since accelerating objects are constantly changing
their velocities- The distance traveled per unit time is not a
constant.
a. Free falling objects accelerate- objects in free fall
will cover a longer distance over each period of time it has fallen
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C. LAW- FOR OBJECTS WITH A
CONSTANT ACCELERATION, THE
DISTANCE OF TRAVEL IS DIRECTLY
PROPORTIONAL TO THE SQUARE OF
THE TIME TRVALED.
1. Object travels twice the time it will
go 4 times the distance.
2. travels 3 times the time, distance is 9
times father.
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II. Calculating acceleration.
A. Ave acceleration= change in
velocity/ time
ave accel= Vf- Vi/t or
ΔV/T
1. units- m/s2 cm/s2 ft/s2
B. Acceleration is a vector- has a
direction
1. Depends if it is speeding up or
slowing down.
2. moving in a positive or
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C. Rule of thumb
1. If the object is slowing down, then the acceleration is
in the opposite direction of motion.
2.can determine if the sign is positive or negative., right
or left, up or down.
a. speeding up- accel is in the same direction as the
velocity so it’s positive
b. slowing down- acceleration is opposite that of the
velocity, so it’s negative
3. direction- when the velocity is increasing in the
direction of the speed- positive accel
4. When an object is slowing down in the direction of the
velocity- negative accel
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Acceleration-A change in velocity
A. A change in speed or direction may occur
1. a= ΔV/ΔT
a. change in velocity/ change in time
2. values may be positive or negative
a. positive speeding up
b. negative slowing down
• II.Velocity of an object with constant
acceleration
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A. Constant acceleration ( uniform)
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1. accel doesn’t change with time
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a. Vf= Vi +at
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III. Displacement during constant
acceleration
A. object is moving at a constant velocity
1. The area under a velocity time
graph
B. d= ½(Vf+ Vi)t
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IV Displacement when acceleration and time are known
A. combine the velocity with constant acceleration and the
displacement during constant acceleration
1. d= ½(Vf+ Vi)T-1/2(Vi+aT)+ Vi-1/2((2Vi+aT)t--
a. d= ViT+1/2at2
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a. ViT= displacement moving at a constant velocity
b. 1/2at2= displacement from rest to and moving
with uniform acceleration
c. the sum of the 2 terms gives the displacement of
an object that starts with an initial velocity and accelerates
uniformly.
2. starting from rest the equation comes down to
d=1/2at2
• B. Velocity-time graph of uniform acceleration- the area
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under the curve equals the displacement.
C. The curve for an accelerating position-time graph is
parabolic
1. When one value increases the other varies as the
square of it.
a. Y= X
D. The slope of a position-time graph of an accelerating
is a tangent point to the parabolic function
1. Calculus people- second derivative function
of the displacement formula
• V. Displacement when velocity and
acceleration are known.
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A. combine the final velocity and
displacement
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1. d=1/2(Vf-Vi)t and Vf= Vi+at,
solve for t and substitute in the first
equation
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a. final equation V2f= V2i +2ad
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VI acceleration due to gravity
A. Galileo- first to show objects fall to the earth with the
same acceleration.
1. Rolled balls down an incline plane which rang bells at
intervals
B. acceleration of gravity is represented by g
1. The acceleration is -9.8m/s2
a. vector- designate up as positive, and down as
negative
b. for each second something drops its speed
increases by 9.8m/s
2. equations for acceleration of gravity
a. Vf=Vi +gt
b. V2f= V2i+ 2gd
c. d= Vi+1/2 gt2