Proving Constant Acceleration's Impact on Average Velocity

In summary, the conversation discusses how to prove that if acceleration is constant, the average velocity is equal to the final velocity plus the initial velocity divided by two. One person suggests drawing a diagram and calculating the average velocity based on the given equations, while another suggests using calculus to find the time average of the velocity function.
  • #1
chocolatelover
239
0

Homework Statement



Prove that if the acceleration is constant, the average velocity=vf+vi/2

Homework Equations


average velocity=xf-xi/change in t
xf=xi+vit+1/2at^2
vf^2=vi^2+2a(xf-xi)



The Attempt at a Solution



I started out by drawing a diagram:

_ _ _ _ _ _ _ _ _
Vi v vf
20km/h 20km/h

20+20/2=20

Do you think this proves it or is there another way of doing it?

Thank you in advance
 
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  • #2
Could someone please help me on this?

Thank you very much
 
  • #3
Can you use calculus or not?
 
  • #4
vf = vi + at
Now if a=constant, the graph of velocity plotted against time is a straight line, yes? (From the equation above)
Now it is obvious that the average velocity between vf and vi must be (vf + vi)/2 from the graph.
Otherwise you can use calculus to find the time average of the velocity function.
 
  • #5
Thank you very much

Regards
 

Related to Proving Constant Acceleration's Impact on Average Velocity

1. How is constant acceleration defined?

Constant acceleration is defined as the rate of change of velocity over time, where the velocity increases or decreases by the same amount every second.

2. How does constant acceleration affect average velocity?

Constant acceleration affects average velocity by causing it to change at a constant rate. This means that the average velocity will increase or decrease by the same amount every second.

3. What is the formula for calculating average velocity with constant acceleration?

The formula for calculating average velocity with constant acceleration is average velocity = (initial velocity + final velocity) / 2.

4. How can constant acceleration be proven to impact average velocity?

To prove the impact of constant acceleration on average velocity, an experiment can be conducted where the acceleration of an object is kept constant while measuring its velocity at different points in time. The data collected can then be used to calculate the average velocity, which should show a consistent increase or decrease, depending on the direction of acceleration.

5. What are some real-world examples of constant acceleration's impact on average velocity?

Some real-world examples of constant acceleration's impact on average velocity include a car accelerating at a constant rate on a straight road, a rollercoaster going down a hill, or a skydiver falling towards the ground. In all of these cases, the average velocity will change at a constant rate due to the constant acceleration.

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