4.1 Acceleration

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4.1 Acceleration
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Chapter Objectives

• Calculate acceleration from the change in speed
  and the change in time.
• Give an example of motion with constant
  acceleration.
• Determine acceleration from the slope of the
  speed versus time graph.
• Calculate time, distance, acceleration, or speed
  when given three of the four values.
• Solve two-step accelerated motion problems.
• Calculate height, speed, or time of flight in
  free fall problems.
• Explain how air resistance makes objects of
  different masses fall with different
  accelerations.

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Chapter Vocabulary

• acceleration
• acceleration due to gravity (g)
• air resistance
• constant acceleration
• delta (?)
• free fall

• initial speed
• m/s2
• term
• terminal velocity
• time of flight
• uniform acceleration

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Inv 4.1 Acceleration

• Investigation Key Question
• How does acceleration relate to velocity?

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4.1 Acceleration

• Acceleration is the rate of change in the speed
  of an object.
• Rate of change means the ratio of the amount of
  change divided by how much time the change takes.

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4.1 Acceleration in metric units

• If a cars speed increases from 8.9 m/s to 27
  m/s, the acceleration in metric units is 18.1
  m/s divided by 4 seconds, or 4.5 meters per
  second per second.
• Meters per second per second is usually written
  as meters per second squared (m/s2).

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4.1 The difference between velocity and
acceleration

• Velocity is fundamentally different from
  acceleration.
• Velocity can be positive or negative and is the
  rate at which an objects position changes.
• Acceleration is the rate at which velocity
  changes.

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4.1 The difference between velocity and
acceleration

• The acceleration of an object can be in the same
  direction as its velocity or in the opposite
  direction.
• Velocity increases when acceleration is in the
  same direction.

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4.1 The difference between velocity and
acceleration

• When acceleration and velocity have the opposite
  sign the velocity decreases, such as when a ball
  is rolling uphill.

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4.1 The difference between velocity and
acceleration

• If both velocity and acceleration are negative
  the speed increases but the motion is still in
  the negative direction.
• Suppose a ball is rolling down a ramp sloped
  downhill to the left.
• Motion to the left is defined to be negative so
  the velocity and acceleration are both negative.
• The velocity of the ball gets LARGER in the
  negative direction, which means the ball moves
  faster to the left.

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4.1 Calculating acceleration

• Acceleration is the change in velocity divided by
  the change in time. The Greek letter delta (?)
  means the change in.

Change in speed (m/sec)
a Dv Dt
Acceleration (m/sec2)
Change in time (sec)
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4.1 Calculating acceleration

• The formula for acceleration can also be written
  in a form that is convenient for experiments.

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Calculating acceleration in m/s2
A student conducts an acceleration experiment by
coasting a bicycle down a steep hill. A partner
records the speed of the bicycle every second for
five seconds. Calculate the acceleration of the
bicycle.

• You are asked for acceleration.
• You are given times and speeds from an
  experiment.
• Use the relationship a (v2 v1) (t2
  t1)
• Choose any two pairs of time and speed data since
  the change in speed is constant.
• a (6 m/s 4 m/s) (3 s 4 s) (2 m/s)
  (-1 s)
• a -2 m/s

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4.1 Constant speed and constant acceleration

• Constant acceleration is different from constant
  speed.
• If an object is traveling at constant speed in
  one direction, its acceleration is zero.
• Motion with zero acceleration appears as a
  straight horizontal line on a speed versus time
  graph.

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4.1 Uniform acceleration

• Constant acceleration is sometimes called uniform
  acceleration.
• A ball rolling down a straight ramp has constant
  acceleration because its speed is increasing at
  the same rate.
• Falling objects also undergo uniform acceleration.

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4.1 Constant negative acceleration

• Consider a ball rolling up a ramp.
• As the ball slows down, eventually its speed
  becomes zero and at that moment the ball is at
  rest.
• However, the ball is still accelerating because
  its velocity continues to change.

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4.1 The speed vs. time graph for accelerated
motion

• In this experiment, velocity and acceleration are
  in the same direction.
• No negative quantities appear, and the analysis
  simply uses speed instead of velocity.

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4.1 Slope and Acceleration

• Use slope to recognize acceleration on speed vs.
  time graphs.
• Level sections (A) on the graph show an
  acceleration of zero.
• The highest acceleration (B) is the steepest
  slope on the graph.
• Sections that slope down (C) show negative
  acceleration (slowing down).

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Calculating acceleration
The graph shows the speed of a bicyclist going
over a hill. Calculate the maximum acceleration
of the cyclist and calculate when in the trip it
occurred.

• You are asked for maximum acceleration.
• You are given a graph of speeds vs. time.
• Use the relationship a slope of graph
• The steepest slope is between 60 and 70 seconds,
  when the speed goes from 2 to 9 m/s.
• a (9 m/s 2 m/s) (10 s)
• a 0.7 m/s2