general physics i motion in one dimension position and...
TRANSCRIPT
Position
• To simplify the study of motion we consider point
particles, i.e., objects that can be represented as a
single point in space. In many cases, real objects
behave as if all their mass is concentrated at one
point, so the point-particle simplification is
reasonable.
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reasonable.
• Motion of a particle occurs when the position of the
particle changes. In one-dimensional (straight-line)
motion, position is specified by a location along the
x (or y) axis, which is taken to be the line along
which the particle moves.
Displacement• Displacement is a difference or change in position.
.if
x x x∆ = −
• The magnitude (absolute
value) tells you the straight-
line distance between the
two points. The sign of the
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two points. The sign of the
displacement tells you the
direction of the motion:
Positive means motion in
the positive x direction
(right); negative means
motion in the negative x
direction (left).
Distance
• If a particle travels 4 meters from A to B and back
to A, the displacement is zero. However, the
distance is not zero. The distance is the total path
length, which is 8 meters for the motion described
above.
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4 meters
B
Average Speed and Average Velocity• Consider a particle that moves between point A and point
B. The average speed of the particle is defined as
A B
xi xf
distanceAverage speed = = .time interval
dt∆
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,displacementtime interval
.ifx av
if
x xxv
t tt=
−∆= =
−∆
xi xf
• Note that the average speed is always positive because the
time interval is always positive and the distance is always
positive (unless the particle did not move at all).
• The average velocity of the particle is defined as
A particle moves 5.8 m along a straight line from point A to point B. The particle then moves back to A. The entire trip takes 5.2 s. Which of the following is true?
1. The average speed is zero and the average velocity is 1.1 m/s.
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2. The average velocity is zero and the average speed is 1.1 m/s.
3. The average velocity is zero and the average speed is 2.2 m/s.
4. The average speed is zero and the average velocity is 2.2 m/s.
Instantaneous Velocity• The average velocity has the same sign, i.e., direction, as the
displacement because the time interval is always positive.
• Note that the average velocity over a finite time interval tells
you nothing about how fast the particle is traveling at any
single point in time (speedometer reading) or the direction at
that instant. The velocity at a single instant in time is called the instantaneous velocity (v ). The instantaneous velocity is
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the instantaneous velocity (vx). The instantaneous velocity is
the average velocity when the time interval is reduced to an
infinitesimally small size. The instantaneous speed is the
magnitude (absolute value) of the instantaneous velocity. The
instantaneous speed is the reading a speedometer gives.
• Like the average velocity, the instantaneous velocity has a
magnitude (size) and a direction (its sign). They are
examples of vector quantities.
Position-Time Graphs
• A position-time (x-t) graph
gives the position of a particle
at every instant in time during
a given time interval.
• The average velocity is the
slope of a straight line drawn
between points representing
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between points representing
the initial and final states of
motion.
• The instantaneous velocity at
an instant in time is the slope
of the tangent to the x-t graph
at that instant.
A person initially at point P in the illustration stays there
a while and then moves along the axis to Q and stays there a
while. She then runs quickly to R, stays there a while, and
then strolls slowly back to P. Which of the position vs. time graphs
below correctly represents this motion?
1. Figure 1.
2. Figure 2.
3. Figure 3.
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3. Figure 3.
4. Figure 4.
5. Figure 5.
6. Figure 6.