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ACCELERATION
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ACCELERATION
• Acceleration: is the rate at which the velocity
of an object changes relative to time
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ACCELERATION
• Acceleration: is the rate at which the velocity
of an object changes relative to change in time
• Acceleration =
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ACCELERATION
• Acceleration: is the rate at which the velocity
of an object changes relative to change in time
• Acceleration =
• Acceleration is a vector
 Because velocity is a vector
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ACCELERATION
• Velocity has speed and direction
Velocity can be changed by:
1. a change in speed
2. a change in direction
3. a change in both speed and direction
Acceleration can occur with:
1. a change in speed
2. a change in direction
3. a change in both speed and direction
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Acceleration means that the speed of an
object is changing, or its direction is, or both.
Acceleration
Acceleration may result in an object either
speeding up or slowing down (or simply changing
its direction).
Acceleration
There is a difference between negative acceleration and
deceleration:
Negative acceleration is acceleration in the negative
direction as defined by the coordinate system.
Deceleration occurs when the acceleration is opposite in
direction to the velocity.
Acceleration
If the acceleration is constant, we can find the velocity as a function of time:
AVERAGE ACCELERATION
• Acceleration =
=
• Acceleration =
•
=
=
=
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AVERAGE ACCELERATION EXAMPLE
• A bicyclist is riding at 15km/hr to the east. In
6.0 seconds he increase his velocity to 45
km/hr to the east.
A. What is the average acceleration of the
bicyclist?
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AVERAGE ACCELERATION EXAMPLE
• A bicyclist is riding at 15km/hr to the east. In 6.0
seconds he increase his velocity to 45 km/hr to the
east.
A. What is the average acceleration of the
bicyclist?
=
E
=
= (30 km/hr )E = 5.0 km/hr
6.0 sec
1.0 sec
East
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AVERAGE ACCELERATION EXAMPLE
• A bicyclist is riding at 15km/hr to the east. In
6.0 seconds he increase his velocity to 45
km/hr to the east.
A. What is the average acceleration of the
bicyclist?
(5.0 km/hr /sec) E
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AVERAGE ACCELERATION EXAMPLE
• A bicyclist is riding at 15km/hr to the east. In
6.0 seconds he increase his velocity to 45
km/hr to the east.
A. What is the acceleration of the bicyclist?
(5.0 km/hr /sec) E
the average change in his velocity was
5.0 km/hr E, in each passing second.
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AVERAGE ACCELERATION EXAMPLE
• A bicyclist is riding at 15km/hr to the east. In
6.0 seconds he increase his velocity to 45
km/hr to the east.
A. What is the acceleration of the bicyclist?
(5.0 km/hr /sec) E
the average change in his velocity was
5.0 km/hr E, in each passing second.
The acceleration of the bicyclist was
probably not uniform
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AVERAGE ACCELERATION
• Acceleration can be positive or negative
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AVERAGE ACCELERATION EXAMPLE
• The same bicyclist is reducing his velocity
AVERAGE ACCELERATION EXAMPLE
• A bicyclist is riding at 45km/hr to the east. In
6.0 seconds he decrease his velocity to
15 km/hr to the east.
A. What is the average acceleration of the
bicyclist?
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AVERAGE ACCELERATION EXAMPLE
• A bicyclist is riding at 45km/hr to the east. In 6.0
seconds he decrease his velocity to
15 km/hr to
the east.
A. What is the average acceleration of the bicyclist?
=
=
E
=
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AVERAGE ACCELERATION EXAMPLE
• A bicyclist is riding at 45km/hr to the east. In
6.0 seconds he decrease his velocity to
15 km/hr to the east.
A. What is the acceleration of the bicyclist?
(-5.0 km/hr /sec) E
the average change in his velocity was
-5.0 km/hr E, in each passing second.
The acceleration of the bicyclist was
probably not uniform
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Instantaneous Acceleration
• The acceleration of an object for a very short
period of time
• Instantaneous Acceleration (a)
• a=
Δ time is approaching zero
• a=
Δt can never be zero, the
equation would be undefined
Instantaneous Acceleration
• The acceleration of an object for a very short
period of time
• Instantaneous Acceleration (a)
• a=
• Instantaneous Acceleration is most often used
when graphing the motion of an object
Acceleration
• When working with acceleration in our course
we will be using CONSTANT ACCELERATION
that is our accelerations will not vary
Acceleration Problems
A train has an initial velocity of 2.1 m/s East. It
accelerates for 15 seconds and achieves a velocity of
3.5 m/s East.
A. What is the acceleration of this train?
B. Convert these velocities into equivalent
km/hr.
Acceleration Problems
A train has an initial velocity of 2.1 m/s East. It
accelerates for 15 seconds and achieves a velocity of
3.5 m/s East.
A. What is the acceleration of this train?
(0.93m/s/s = 0.93m/s2
B. Convert these velocities into equivalent
km/hr.
Acceleration Problems
A train has an initial velocity of 2.1 m/s East. It
accelerates for 15 seconds and achieves a velocity of
3.5 m/s East.
A. What is the acceleration of this train?
(0.93m/s/s = 0.93m/s2
B. Convert these velocities into equivalent
km/hr.
2.1 m/s
7.6 km/hr
3.5 m/s
13 km/hr
Acceleration Due to Gravity
• Acceleration due to gravity in a FREE FALL
A FREE FALL occurs when a mass is falling
solely under the force of gravity
Figure 2-14
Free fall and air resistance
Acceleration Due to Gravity
• Acceleration due to gravity in a FREE FALL
A FREE FALL occurs when a mass is falling
solely under the force of gravity
Acceleration Due to Gravity
• Acceleration due to gravity in a FREE FALL
A FREE FALL occurs when a mass is falling
solely under the force of gravity
No air resistance is occurring
Acceleration Due to Gravity
• Acceleration due to gravity in a FREE FALL
A FREE FALL occurs when a mass is falling
solely under the force of gravity
No air resistance is occurring
Only gravity is influencing a mass’s
change in velocity
Acceleration Due to Gravity
• Acceleration due to gravity in a FREE FALL
A FREE FALL occurs when a mass is falling
solely under the force of gravity
No air resistance is occurring
Only gravity is influencing a mass’s
change in velocity
This does not happen on earth
Acceleration Due to Gravity
• Acceleration due to gravity in a FREE FALL
A FREE FALL occurs when a mass is falling
solely under the force of gravity
No air resistance is occurring
Only gravity is influencing a mass’s
change in velocity
This does not happen on earth, but
we pretend that it does for simplicity
Acceleration Due to Gravity
• Free Fall near Earth’s Surface
Acceleration of the mass is -9.81 m/s2
a = g = -9.81 m/s2
Acceleration Due to Gravity
• Free Fall near Earth’s Surface
Acceleration of the mass is -9.81 m/s2
a = g = -9.81 m/s2
This acceleration varies slightly by location
dependent on
radius of earth at particular location
density of earth at particular location
Acceleration Due to Gravity
• Free Fall near Earth’s Surface
Acceleration of the mass is -9.81 m/s2
a = g = -9.81 m/s2
This acceleration varies slightly by location
dependent on
radius of earth at particular location
density of earth at particular location
As distance above earth’s surface increases the
acceleration due to earth’s gravity decreases
Acceleration Due to Gravity
• Free Fall near Earth’s Surface
Acceleration of the mass is -9.81 m/s2
a = g = -9.81 m/s2
This acceleration varies slightly by location
dependent on
radius of earth at particular location
density of earth at particular location
As distance above earth’s surface increases the
acceleration due to earth’s gravity decreases
More on this later in the course
Acceleration Due to Gravity
Earth
Acceleration Due to Gravity
• The gravitational acceleration is about -9.8m/s2 for a
very small distance above the earth’s surface
• Not to scale
Earth
Acceleration Due to Gravity
• The gravitational acceleration is about 9.8m/s2 for a
very small distance above the earth’s surface
• After about 12 km it becomes≈ 9.79m/s2
• Not to scale
Earth
Acceleration Due to Gravity
• The gravitational acceleration is about -9.8m/s2 for a
very small distance above the earth’s surface
• After about +12 km it becomes≈ -9.79m/s2
• As distance above earth increases this rate of
gravitational acceleration decreases.
• Not to scale
Earth
Acceleration Due to Gravity
• The gravitational acceleration is about -9.8m/s2 for a
very small distance above the earth’s surface
• After about +12 km it becomes≈ -9.79m/s2
• A distance above earth increases this rate of
gravitational acceleration decreases.
• g will never reach zero
• Not to scale
Earth
Gravitational Problems
• A ball is dropped from the top of a tall
building.
A.What is the original velocity of the ball?
A. What is its velocity in m/s after it falls for 5.0
seconds?
B. Why isn’t air resistance factored into our
answer?
Gravitational Problems
• A ball is dropped vertically from the top of a
tall building.
A.What is the original vertical velocity of the ball?
zero m/s, it was dropped NOT thrown vertically
A. What is its velocity in m/s after it falls for 5.0
seconds?
B. Why isn’t air resistance factored into our
answer?
Gravitational Problems
• A ball is dropped vertically from the top of a
tall building.
A.What is the original vertical velocity of the ball?
zero m/s, it was dropped NOT thrown vertically
A. What is its velocity in m/s after it falls for 5.0
seconds? -49 m/s
B. Why isn’t air resistance factored into our
answer?
Gravitational Problems
• A ball is dropped vertically from the top of a
tall building.
A.What is the original vertical velocity of the ball?
zero m/s, it was dropped NOT thrown vertically
A. What is its velocity in m/s after it falls for 5.0
seconds? -49 m/s
B. Why isn’t air resistance factored into our
answer? We ignore air resistance in this
course