Chapter 2-Section 1
1-Dimensional Kinematics
The motion of
automobiles, Hot Wheel
cars, and rockets are
used to illustrate the
physics of position,
velocity, acceleration, and
kinematic graphing.
Kinematics
Kinematics is the science of describing
the motion of objects using words,
diagrams, numbers, graphs, and
equations.
Motion
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Motion happens all around us.
One – dimensional motion is the
simplest form of motion.
The object can only move in one
dimension
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forward and backward
left and right
up and down
Motion
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Motion takes place over time and depends on
a frame of reference.
Frame of Reference – a coordinate system for
specifying the precise location of objects in
space
The choice of a reference point is arbitrary,
but once chosen, the same point must be
used throughout the problem.
Distance and Displacement
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Distance and displacement are two quantities
which may seem to mean the same thing, yet
they have distinctly different meanings and
definitions.
Distance is a scalar quantity which refers to
"how much ground an object has covered"
during its motion.
Displacement is a vector quantity which
refers to "how far out of place an object is"; it
is the object's change in position.
Distance and Displacement
To test your understanding of this distinction,
consider the motion depicted in the diagram
below. A physics teacher walks 4 meters East,
2 meters South, 4 meters West, and finally 2
meters North.
Distance traveled = 12 m
Displacement = 0 m
Distance and Displacement
The diagram below shows the position of a cross-country skier at
various times. At each of the indicated times, the skier turns around
and reverses the direction of travel. In other words, the skier moves
from A to B to C to D. Use the diagram to determine the distance
traveled by the skier and the resulting displacement during these three
minutes.
Distance traveled =
420 m
Displacement = 140 m
Seymour Butz views football games from under the bleachers. He
frequently paces back and forth to get the best view. The diagram
below shows several of Seymour's positions at various times. At each
marked position, Seymour makes a "U-turn" and moves in the
opposite direction. In other words, Seymour moves from position A
to B to C to D. What is Seymour's resulting displacement and
distance of travel?
Distance = 95 yards
Displacement = 55yards
Displacement
Δx = xf – xi
Displacement = change in position
Displacement = final position – initial position
Speed and Velocity
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Speed is a scalar quantity
which refers to "how fast
an object is moving.“
Velocity is a vector quantity
which refers to "the rate at
which an object changes its
position."
Speeding Little Old Lady
Average Speed and Velocity
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Average speed is the total distance traveled divided by
the time interval
Average velocity is the total displacement traveled
divided by the time interval during which the
displacement occurred
While on vacation, Lisa Carr traveled a total
distance of 440 miles. Her trip took 8 hours.
What was her average speed?
Ave speed = distance traveled
time of travel
Ave speed = 440 mi
8h
Ave speed = 55 mi / h
Problem
A car travels from city A to city B
(100km). If the first half of the
distance is driven at 50 km/h and the
second half is driven at 100 km/h ,
what is the average velocity for the
trip?
A
100 km
V = 50 km/h
B
V = 100 km/h
t = d/s
t = 50 km
50 km/h
t=1h
t = d/s
t = 50 km
100 km/h
t = 0.5 h
Ave. velocity = displacement
time
Ave velocity = 100 km
1.5 h
67 km/h
Velocity
Constant Velocity – velocity is unchanging
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Instantaneous Velocity – the velocity of an
object at some instant (or specific point in its
path) (slope)
Homework
Describing Motion with Position vs. Time Graphs
The Meaning of Shape for a
position-time Graph
The specific features of the motion of objects are demonstrated
by the shape and the slope of the lines on a position vs. time
graph.
If the positiontime data for
such a car were
graphed, the
resulting graph
would look like
the graph at the
right.
If the position-time
data for such a car
were graphed, the
resulting graph would
look like the graph at
the right.
The position vs. time graphs for the two types of motion
– constant velocity and changing velocity
Positive constant velocity
Positive changing velocity
The Principle of Slope for a p–t Graph
The slope of the line on a position-time
graph reveals useful information about
the velocity of the object. It's often
said, "As the slope goes, so goes the
velocity."
Let me test your understanding
Match the slope with the velocity
Positive slope
Constant slope
Small slope
Small velocity
Positive velocity
Constant velocity
Answers :
Positive slope
Positive velocity
Constant slope
Constant velocity
Small slope
Small velocity
Slow rightward,
Constant velocity
Fast, rightward,
Constant velocity
Fast, leftward
Constant velocity
Slow , leftward
Constant velocity
Leftward velocity,
Slow to fast
Leftward velocity,
Fast to slow
The Passing Lane
Constant Positive Velocity
Constant Negative Velocity