# Average and Final Velocity

I got this problem and it just stumped me. Can anyone give me the solution? Anyways, here's the question:
Show that the average velocity of a body undergoing constant acceleration, and starting from rest. is half of its final velocity.

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i was trying to solve your problem with some made up #'s but i couldn't get the V average to equal Vf. It may be my methods.....

Sounds like you're already given the solution. The trick is getting there, right?

Why don't you show us what you've tried so far?

well if you take the initial V plus the final V and average it out your going to get the average V. (0+Vf)/2=1/2Vf I hope that helps

NateTG
Homework Helper
There's a nifty equation for constant acceleration which essentially gives you the answer.

$$\vec{x}=\vec{x}_0+\frac{\vec{v}_0+\vec{v}}{2}t$$

You can also derive it from:
$$\vec{x}=\vec{x}_0+\vec{v}_0t+\frac{1}{2}\vec{a}t^2$$
and
$$\vec{v}=\vec{v}_0+\vec{a}t$$
by solving the bottom equation for $$t$$ and substituting in to the top one.

HallsofIvy