Kinematics
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Distance – the total measured path that an object
travels. (scalar)
Displacement – the measured straight line distance
from when the object starts to where it ends. (vector,
watch for negatives)
Speed – distance traveled divided by total time of
travel or rate of change of position (scalar)
Velocity – Displacement divided by total time or rate
of change of displacement. (vector, watch for
negatives)
Acceleration – rate of change of velocity (vector, +
increasing velocity, negative decreasing velocity in
horizontal motion)
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Average velocity is the total displacement divided by
total time. There could be many different velocities that
occur during the trip that are not equal to the ave
velocity.
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Instantaneous velocity is the exact velocity at a particular
moment. This can be found as the change in time
approaches 0. The smaller the time interval the more
accurate the inst velocity.
Ave velocity can also be found with:
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This assumes that each velocity was maintained for an
equal amount of time.
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Slope of a position time graph = velocity
Slope of a velocity time graph = acceleration
Area under acceleration time graph = ave. velocity
Area under velocity time graph = displacement.
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Analyze the slope as being positive or
negative since all of the these are vectors.
For curved lines, the change in the slope
(tangent line) gives you a clue to the motion
of the object too.
Keep in mind, we do not deal with changing
accelerations. Therefore we will not see any
slope on an acceleration vs time graph.
The left side deals with horizontal motion and the right side deals with vertical
motion.
Common strategies:
-List your known variables and the variable you are looking to find.
-Look for an equation that includes of those variables.
-If one does not exist, can you solve for a different unknown that will help?
-Can you solve an equation for an unknown and substitute it in to another equation?
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Use the equations below.
Acceleration will most likely be acceleration
due to gravity -9.8m/s2
If an object is falling its velocity is negative
and so is the displacement.
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vx is constant during the entire
parabolic path.
Initial vertical velocity is 0 and
increase due to g.
Use kinematics equations to solve.
Time for an object drop from height
y is equal to the time for an object to
hit the ground when launched
horizontally from height y.
You can solve for time in terms of
horizontal and vertical
displacements and set them equal to
each other.
Only height affects launch time, not
horizontal v.
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First step is to find the vertical and horizontal
components of the original launch v. Launch v
will not be used again.
Horizontal v stays constant. Vertical v
decreases(but +) on the way up, is zero at the
top of the path and increases(but -) on the way
down.
For t, we know final vertical v at the top is 0.
solve for time to that point and then t up = t
down.
When dealing with vertical unknowns such as
max height. We always go to the peak of the
path.
Range = horizontal v x total time.
Max range when angle = 45
Max time in air when angle = 90
2 angles equidistant fro 45 degrees will have the
same range. Ie. 10 and 80 or 30 and 60.
Centripetal force and centripetal
acceleration are directed toward
the center of the path.
 Centripetal force is not a real
force and should therefore not be
labeled on an FBD, it must be
caused by something. EX gravity,
friction etc.
 Velocity is directed tangentially
to the path of motion as shown in
the diagram.
 The “force” direction away from
the center of the path is due to
the inertia of the object wanting
to continue in a straight line.
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In many problems, two objects are either approaching
each other, chasing each other, or trying to get away
from each other. Some examples might be: a police
car chasing a speeding car, a passenger chasing a
departing train or bus, an ambulance moving through
traffic, two cars moving through an intersection, two
vehicles coming towards each other on a two-line
road, or two one-dimensional projectiles traveling in
the same or opposite directions while moving through
the air.
xpursuer = "gap" + xleader
vot + ½at2
number
vot + ½at2
vt
vt
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Each column in the above table states the allowed
behaviors for the pursuer and the leader. Each participant
can either be experiencing accelerated or linear motion.
The numerical value of the "gap" can be equal to zero (if
the two objects start side-by-side) or it can be a nonzero
number. The parameter t, for time, unites the equations.
To solve chase equations, you first determine the time
that is required for the two objects to come together then, you use that time to determine the position of their
collision.
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To work this type of problem, one object is considered the
leader and the other is the pursuer. The pursuer, in
reaching the leader's final location, must not only close
the leader's original gap but also account for any
subsequent displacement the leader travels while being
chased.
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In a swimming race, a father gives his 4 year old
son a 10-second head-start. The pool is 25meters long. The child swims at 0.80 m/sec
while the father swims at 1.20 m/sec.
 How far is the child ahead of the father when the
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father gets to start swimming?
What chase equation must you solve to determine
the winner?
At what time does the father come up alongside his
son?
How far has the father swum at that point?
Who wins the race?
Describe the s-t graph for this problem.
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How far is the child ahead of the father when
the father gets to start swimming?
x = vt
x = (0.8)(10)
x = 8 meters
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What chase equation must you solve to
determine the winner?
1.20m/s t = 8m + 0.8m/s t
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At what time does the father come up
alongside his son?
1.2m/s t = 8m + 0.80m/s t
0.4m/s t = 8m
t = 20 seconds
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How far has the father swum at that point?
x = vt
x = (1.20m/s)(20s)
x = 24 meters
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Who wins the race?
The father out touches his son by 0.42 seconds.
There is one meter left to swim when the father
comes up alongside his son. The father will travel
that meter in 1 m / 1.2 m/sec = 0.833 second. The
son will travel that final meter in 1 m / 0.8 m/sec
= 1.25 seconds. Subtracting we find that the
father will win by 0.42 seconds.
The father wins the race and “Father of The
Year” for beating his 4 year old son.