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Negative Acceleration help

  1. Sep 20, 2009 #1
    I need some negative acceleration help. I know that negative acceleration does not mean that the object is slowing down. However, there is a negative acceleration when the slope of the velocity vs. time graph is negative. Except, when there is this negative slope, the velocity is getting lower. So, even though the velocity is getting lower, is it negatively accelerating?

    I am confused. Because how can the object not be slowing down when there is negative acceleration? How does it relate to the ball rolled up an incline? If the ball is rolling back down the plank, the velocity is negative, so is the acceleration negative because the velocity is negative?

    Thanks
     
  2. jcsd
  3. Sep 20, 2009 #2

    kuruman

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    "Negative" is really a convention. One definition is "up" is "positive" and "down" is negative in which case the acceleration of gravity is negative. Another definition for "positive" is "in the same direction as the velocity". In that case the acceleration of gravity is "negative" if a thrown object is moving "up" and "positive" if it is moving "down".

    Regardless of definition, however, when the acceleration is in the same direction as the velocity, the speed increases; when the acceleration is opposite to the direction of the velocity, the speed decreases. That's what really counts.
     
  4. Sep 20, 2009 #3
    If you toss a ball vertically into the air it moves in the (+) up direction but as it does so, it is decreasing in velocity in the (+) direction. When the ball reaches its maximum height its velocity is zero (so on a velocity v. time graph you would see a line going from an initial positive velocity to zero.

    Now as the ball begins to descend, the velocity in the negative (down) direction increases. So the ball is increasing in speed and it velocity is increasing in the negative direction. Same thing if you push an object up a frictionless slope... (on a velocity v. time graph the line would continue below the 0m/s mark and into the negative velocity part of the graph or below your horizontal time axis.

    You might have been thinking of a car slowing down and coming to a halt, but the car will not come back in the negative direction unless you unless you threw it into reverse to cause it to slow, come to a halt, and then increase in speed back to where you started and even beyond...

    Hope these examples help.
     
  5. Sep 20, 2009 #4
    This is a tricky point, you need to understand the difference between speed and velocity.

    This is more a question of linguistics and intuition than it is one of physics.
    What's getting you mixed up is the difference between an increase in magnitude, and an increase relative to some system of axis (Becoming "more positive")

    Speed is just how fast an object is moving, what the magnitude of its velocity is.
    Velocity, on the other hand, is a vector quantity. That means that it has a magnitude as well as a direction!

    Acceleration is change in velocity, not in speed (Though a change in speed does follow from this)

    Let's take a couple of example cases, for all of these, I will use a right-handed coordinate system (Positive x is pointing right)

    1. An object is traveling right with an initial velocity of 100 m/s. It is accelerated by a positive acceleration (Positive means pointing right, in the direction of the positive x axis)

    Its speed will increase, the magnitude of its velocity will increase, and the direction will remain the same.

    2. An object is traveling left with an initial velocity of -100 m/s. It is accelerated by a positive acceleration. (The initial velocity vector points left, while the acceleration vector points right)

    The velocity will become "more positive," but you can plainly see that the magnitude of the velocity, the speed of the object, will decrease.


    3. An object is traveling left with an initial velocity of -100 m/s. It is accelerated by a negative acceleration. (The initial velocity vector points left, and the acceleration vector points left as well)

    The velocity will become "more negative," decreasing, so to speak, but you see that the speed increases, instead of decreasing.
     
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