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Copyright © 2012 Pearson Education Inc.
PowerPoint® Lectures for
University Physics, Thirteenth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Chapter 2
Motion Along a
Straight Line
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 2
• To describe straight-line motion in terms of velocity and
acceleration
• To distinguish between average and instantaneous velocity
and average and instantaneous acceleration
• To interpret graphs of position versus time, velocity versus
time, and acceleration versus time for straight-line motion
• To understand straight-line motion with constant
acceleration
• To examine freely falling bodies
• To analyze straight-line motion when the acceleration is
not constant
Copyright © 2012 Pearson Education Inc.
Introduction
• Kinematics is the study of motion.
• Velocity and acceleration are important physical
quantities.
• A bungee jumper speeds up during the first part of his
fall and then slows to a halt.
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Displacement, time, and average velocity—Figure 2.1
• A particle moving along the x-axis has a coordinate x.
• The change in the particle’s coordinate is x = x2 x1.
• The average x-velocity of the particle is vav-x = x/t.
• Figure 2.1 illustrates how these quantities are related.
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Negative velocity
• The average x-velocity is negative during a time interval if
the particle moves in the negative x-direction for that time
interval. Figure 2.2 illustrates this situation.
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A position-time graph—Figure 2.3
• A position-time graph (an x-t graph) shows the particle’s position x as a function of time t.
• Figure 2.3 shows how the average x-velocity is related to the slope of an x-t graph.
Copyright © 2012 Pearson Education Inc.
Instantaneous velocity—Figure 2.4
• The instantaneous velocity is the velocity at a
specific instant of time or specific point along the
path and is given by vx = dx/dt.
• The average speed is not the magnitude of the
average velocity!
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Average and instantaneous velocities
• In Example 2.1, the cheetah’s instantaneous velocity
increases with time. (Follow Example 2.1)
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Finding velocity on an x-t graph
• At any point on an x-t graph, the instantaneous x-
velocity is equal to the slope of the tangent to the
curve at that point.
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Motion diagrams
• A motion diagram shows the position of a particle at various instants, and arrows represent its velocity at each instant.
• Figure 2.8 shows the x-t graph and the motion diagram for a
moving particle.
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Instantaneous acceleration
• The instantaneous acceleration is ax = dvx/dt.
• Follow Example 2.3, which illustrates an accelerating racing
car.
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Finding acceleration on a vx-t graph
• As shown in Figure 2.12, the x-t graph may be used to
find the instantaneous acceleration and the average
acceleration.
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A vx-t graph and a motion diagram
• Figure 2.13 shows the vx-t graph and the motion diagram
for a particle.
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An x-t graph and a motion diagram
• Figure 2.14 shows the x-t graph and the motion diagram
for a particle.
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Motion with constant acceleration—Figures 2.15 and 2.17
• For a particle with constant acceleration, the velocity
changes at the same rate throughout the motion.
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Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
A motorcycle with constant acceleration
• Follow Example 2.4 for an accelerating motorcycle.
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Copyright © 2012 Pearson Education Inc.
Two bodies with different accelerations
• Follow Example 2.5 in which the police officer and
motorist have different accelerations.
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Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Freely falling bodies
• Free fall is the motion of
an object under the
influence of only gravity.
• In the figure, a strobe
light flashes with equal
time intervals between
flashes.
• The velocity change is
the same in each time
interval, so the
acceleration is constant.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
A freely falling coin
• Aristotle thought that heavy
bodies fall faster than light
ones, but Galileo showed that
all bodies fall at the same rate.
• If there is no air resistance, the
downward acceleration of any
freely falling object is g = 9.8
m/s2 = 32 ft/s2.
• Follow Example 2.6 for a coin
dropped from the Leaning
Tower of Pisa.
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Up-and-down motion in free fall
• An object is in free
fall even when it is
moving upward.
• Follow Example 2.7
for up-and-down
motion.
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Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Copyright © 2012 Pearson Education Inc.
Is the acceleration zero at the highest point?—Figure 2.25
• The vertical
velocity, but not
the acceleration,
is zero at the
highest point.
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Two solutions or one?
• We return to the ball in the previous example.
• How many solutions make physical sense?
• Follow Example 2.8.
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Velocity and position by integration
• The acceleration of a car is not always constant.
• The motion may be integrated over many small time intervals to
give .00 0
and t t
x ox x xv v a dt x x v dt
Copyright © 2012 Pearson Education Inc.
Motion with changing acceleration
• Follow Example 2.9.
• Figure 2.29 illustrates the motion graphically.
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