Proving Constant Acceleration's Impact on Average Velocity

[chocolatelover]

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

 

[chocolatelover]

Could someone please help me on this?

Thank you very much

 

[qspeechc]

Can you use calculus or not?

 

[qspeechc]

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.

 

[chocolatelover]

Thank you very much

Regards