Average Velocity and Constant Acceleration

In summary, the equation Vav=(Vi+Vf)/2 is not only valid for constant acceleration, but can also be true for variable acceleration. This is because any velocity function with the same amount of area under the curve as a constant acceleration function will also yield the same average velocity.
  • #1
Can some one please prove that Vav=(Vi+Vf)/2 is valid only for constant acceleration?
 
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  • #2
Ali Asadullah said:
Can some one please prove that Vav=(Vi+Vf)/2 is valid only for constant acceleration?
No, because it isn't valid only for constant acceleration. There are other velocity functions that also yield this average velocity.
 
  • #3
Ali Asadullah said:
Can some one please prove that Vav=(Vi+Vf)/2 is valid only for constant acceleration?
It's posible for Vav=(Vi+Vf)/2 to be true for variable acceleration as well. Start off with a graph of velocity (y axis) versus time (x axis). Then the area below the horizontal line that goes from {t0, Vav} to {t1, Vav} = Vav x (t1 - t0) = the distance traveled. Then note that any line of any shape with the same amount of area under the line from {t0, Vi} to {t1, Vf} would also have the same average velocity as constant acceleration.
 

1. What is the difference between average velocity and constant acceleration?

Average velocity is the overall displacement of an object divided by the total time it took to travel that distance. Constant acceleration, on the other hand, is the rate at which an object's velocity changes over time. While average velocity is a measure of the overall displacement, constant acceleration is a measure of the change in velocity.

2. How is average velocity calculated?

Average velocity is calculated by dividing the total displacement of an object by the total time it took to travel that distance. The formula for average velocity is: average velocity = total displacement / total time.

3. What is the relationship between velocity and acceleration?

Velocity and acceleration are related in that acceleration is the rate of change of velocity over time. This means that any change in an object's velocity, whether it is speeding up, slowing down, or changing direction, is considered acceleration.

4. Can an object have a constant acceleration but varying velocity?

Yes, an object can have a constant acceleration but varying velocity. This can occur when the object is moving at a constant rate but in different directions, such as in circular motion. In this case, although the object's acceleration remains constant, its velocity continuously changes due to the change in direction.

5. How does constant acceleration affect an object's motion?

Constant acceleration causes an object to change its velocity by the same amount every second. This means that the object's speed will either increase or decrease at a constant rate. This type of motion is known as uniformly accelerated motion and follows the equations of motion: v = u + at, s = ut + 1/2at², and v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, t is the time, and s is the displacement.

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