Frame of Reference
A coordinate frame is required in order to describe motion.
The motion of an object is described relative to this
coordinate frame of reference.
In this course our frame of reference will be the Cartesian
Coordinate System.
Arrrrg!! Me palm tree….Matey!
Positive and Negative Displacement
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Depends on your frame of reference.
Convention is:
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Moving right is positive, +x, 0°, East
Moving left is negative, -x, 180°, West
Moving up is positive, +y, 90°, North
Moving down is negative, -y, 270°, South
Velocity
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Kinematics - The branch of mechanics that studies
bodies undergoing change of position (displacement).
Velocity-The rate of change of an object’s position.
Scalar-a quantity with magnitude but no direction.
–
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Vector- a quantity with magnitude and direction.
–
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Examples: mass, temperature, energy, speed, distance
Examples: displacement, velocity, force, acceleration
5 miles – vector or scalar?
5 miles, north –vector or scalar?
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45o C – vector or scalar?
28.34 g ?
12 N (Newtons) at 045o ?
320 birds ?
East ?
5 miles, west ?
300 J (joules)
45 miles per hour ?
2.54 cm ?
Distance and Displacement

Distance is a scalar quantity
–

How much ground an object has covered.
Displacement is a vector quantity
–
Change in position, from the origin in the frame of
reference.
Question?????
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
What is the distance of cars in the INDY
500?
What is displacement of cars in the INDY
500?
Use problem solving techniques to
solve this problem
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A cross country skier goes in the positive X direction
180 meters for one minute
He reverses direction(-) and goes 140 meters for
another minute.
He reverses again (+) and goes 100 meters for
another minute.
What is his distance?
What is his displacement? (remember to express
direction)
Speed and Velocity
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Speed is a scalar quantity
Velocity is a vector quantity.
The direction of the velocity vector is the
same as the change of displacement vector.
Velocity = change in position/time
velocity = displacement/time
Speed = distance/time
From the previous skier problem, what is the skiers
speed?
What is the skier’s velocity?
The wander’s journal
Average and Constant Velocity
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Average velocity is the change in position
(displacement) divided by the time interval over
which the change occurred.
Vavg = ∆d/ ∆t = (df – di)/(tf – ti) = rise / run

If the average velocity of an object does not
change, then the object is moving at constant
velocity. Constant velocity is also called uniform
velocity.
Average and Constant Velocity

IF…and ONLY IF….the velocity changes
uniformly, we can also calculate average velocity
with:
Vf  Vi

V avg 2
Instantaneous Velocity

Instantaneous velocity is the average velocity
over a very tiny interval of time (approaching
zero seconds).
Graphically, it is the slope of the tangent to a
position-time graph at a point.
Picturing Motion:Position Time Graphs
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A Displacement Time Graph (d-t graph) describes the
motion of an object by showing the change in position
in relation to time.
The slope of the position time is the velocity of the
object.
Speed & Velocity

Average, Instantaneous, Constant
1. Describe the motion of each car.
2. Give the velocity of car A at
a.
b.
c.
t=3s
t=5s
t = 10 s
3. Car B at:
a.
b.
t=7s
the interval between t = 0 and t = 10 sec
4. Car C at:
a.
b.
c.
t=7s
t=9s
the interval between t = 0 and t = 10 sec
5. Give the velocity of Car D at:
a.
the interval between t = 0 and t = 10 sec
6. Car E at:
a. the interval between t = 0 and t = 8 sec
b. the interval between t = 8 and t = 10 sec
c. the interval between t = 0 and t = 10 sec
Calculating Displacement
from Average Velocity

The average velocity equation can be rearranged to
calculate displacement
Vavg = ∆d/ ∆t
Vavg(∆t) = ∆d

If velocity changes at an even (uniform) rate, we can
still use this equation by substituting average velocity
for Vavg
Vf  Vi
(t )  d
2
Problems
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Example Problems, page 61
#17, #18, #20