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Acceleration

           Acceleration, Speed and Velocity
Acceleration is the rate of change of velocity.
   When the velocity of an object changes, the
   object is accelerating.


A change in velocity can be either a change in
   how fast something is moving, or a change
   in the direction it is moving.


 Acceleration occurs when an object changes its
    speed, it's direction, or both.
Acceleration

           Speeding Up and Slowing Down
When you think of acceleration, you probably think of something speeding up.
  However, an object that is slowing down also is accelerating.
Acceleration also has direction, just as velocity does.
Acceleration

           Speeding Up and Slowing Down
If the acceleration is in the same direction as the velocity,


  the speed increases and
   the acceleration is
   positive.
Acceleration

           Speeding Up and Slowing Down
If the speed decreases, the acceleration is in the opposite



  direction from the
   velocity, and the
   acceleration is negative.
Acceleration

           Changing Direction
A change in velocity can be either a change in how fast something is moving or a
   change in the direction of movement.

Any time a moving object changes direction, its velocity changes and it is
   accelerating.
Acceleration

          Changing Direction
The speed of the horses in this
   carousel is constant, but the
   horses are accelerating because
   their direction is changing
   constantly.
Acceleration

            Calculating Acceleration
To calculate the acceleration of an object, the change in velocity is divided by the
    length of time interval over which the change occurred.




To calculate the change in velocity, subtract the initial velocity—the velocity at the
    beginning of the time interval—from the final velocity—the velocity at the end
    of the time interval.
Acceleration

           Calculating Acceleration
If the direction of motion doesn't change and the object moves in a straight line,
     the change in velocity is the same as the change in speed.




The change in velocity then is the final speed minus the initial speed.
Acceleration

           Calculating Positive Acceleration

How is the acceleration for an object that is speeding up different from that of an
  object that is slowing down?




Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80
   m/s in 20 s.
Acceleration

            Calculating Positive Acceleration
The airliner is traveling in a straight line down the runway, so its speed and velocity
   are the same.




Because it started from
   rest, its initial speed
   was zero.
Acceleration
2.2

            Calculating Positive Acceleration
 Its acceleration can be calculated as follows:
Acceleration
2.2

            Calculating Positive Acceleration
 The airliner is speeding up, so the
    final speed is greater than the
    initial speed and the acceleration
    is positive.
Acceleration
2.2

               Calculating Negative Acceleration
 Now imagine that a skateboarder is moving in a straight line at a constant speed of
   3 m/s and comes to a



      stop in 2 s.


 The final speed is zero and the
    initial speed was 3 m/s.
Acceleration

           Calculating Negative Acceleration
The skateboarder's acceleration is calculated as follows:
Acceleration

           Calculating Negative Acceleration
The skateboarder is slowing down, so the final speed is less than the initial speed
   and the acceleration is



  negative.

The acceleration always will be positive
   if an object is speeding up and
   negative if the object is slowing
   down.
Acceleration

          Amusement Park Acceleration
Engineers use the laws of physics to design amusement park rides that are
   thrilling, but harmless.



The highest speeds and
   accelerations usually are
   produced on steel roller
   coasters.
Acceleration

           Amusement Park Acceleration
Steel roller coasters can offer multiple steep drops and inversion loops, which give
   the rider large accelerations.




As the rider moves down a steep hill or an inversion loop, he or she will accelerate
    toward the ground due to gravity.
Acceleration
2.2

            Amusement Park Acceleration
 When riders go around a sharp turn, they also are accelerated.




 This acceleration makes them feel as if a force is pushing them toward the side
    of the car.

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Acceleration

  • 1. Acceleration Acceleration, Speed and Velocity Acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating. A change in velocity can be either a change in how fast something is moving, or a change in the direction it is moving. Acceleration occurs when an object changes its speed, it's direction, or both.
  • 2. Acceleration Speeding Up and Slowing Down When you think of acceleration, you probably think of something speeding up. However, an object that is slowing down also is accelerating. Acceleration also has direction, just as velocity does.
  • 3. Acceleration Speeding Up and Slowing Down If the acceleration is in the same direction as the velocity, the speed increases and the acceleration is positive.
  • 4. Acceleration Speeding Up and Slowing Down If the speed decreases, the acceleration is in the opposite direction from the velocity, and the acceleration is negative.
  • 5. Acceleration Changing Direction A change in velocity can be either a change in how fast something is moving or a change in the direction of movement. Any time a moving object changes direction, its velocity changes and it is accelerating.
  • 6. Acceleration Changing Direction The speed of the horses in this carousel is constant, but the horses are accelerating because their direction is changing constantly.
  • 7. Acceleration Calculating Acceleration To calculate the acceleration of an object, the change in velocity is divided by the length of time interval over which the change occurred. To calculate the change in velocity, subtract the initial velocity—the velocity at the beginning of the time interval—from the final velocity—the velocity at the end of the time interval.
  • 8. Acceleration Calculating Acceleration If the direction of motion doesn't change and the object moves in a straight line, the change in velocity is the same as the change in speed. The change in velocity then is the final speed minus the initial speed.
  • 9. Acceleration Calculating Positive Acceleration How is the acceleration for an object that is speeding up different from that of an object that is slowing down? Suppose a jet airliner starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s.
  • 10. Acceleration Calculating Positive Acceleration The airliner is traveling in a straight line down the runway, so its speed and velocity are the same. Because it started from rest, its initial speed was zero.
  • 11. Acceleration 2.2 Calculating Positive Acceleration Its acceleration can be calculated as follows:
  • 12. Acceleration 2.2 Calculating Positive Acceleration The airliner is speeding up, so the final speed is greater than the initial speed and the acceleration is positive.
  • 13. Acceleration 2.2 Calculating Negative Acceleration Now imagine that a skateboarder is moving in a straight line at a constant speed of 3 m/s and comes to a stop in 2 s. The final speed is zero and the initial speed was 3 m/s.
  • 14. Acceleration Calculating Negative Acceleration The skateboarder's acceleration is calculated as follows:
  • 15. Acceleration Calculating Negative Acceleration The skateboarder is slowing down, so the final speed is less than the initial speed and the acceleration is negative. The acceleration always will be positive if an object is speeding up and negative if the object is slowing down.
  • 16. Acceleration Amusement Park Acceleration Engineers use the laws of physics to design amusement park rides that are thrilling, but harmless. The highest speeds and accelerations usually are produced on steel roller coasters.
  • 17. Acceleration Amusement Park Acceleration Steel roller coasters can offer multiple steep drops and inversion loops, which give the rider large accelerations. As the rider moves down a steep hill or an inversion loop, he or she will accelerate toward the ground due to gravity.
  • 18. Acceleration 2.2 Amusement Park Acceleration When riders go around a sharp turn, they also are accelerated. This acceleration makes them feel as if a force is pushing them toward the side of the car.