# Average velocity question

1. Jul 22, 2009

### demonelite123

i was just wondering how do you prove that

average velocity = (initial velocity + final velocity) / 2

when the acceleration is constant.

my book simply tells me the formula and how to use it but doesn't say how it got this formula in the first place.

2. Jul 22, 2009

### RoyalCat

How would you define average velocity?
What distance will you travel, starting at the initial velocity, under constant acceleration, over a time of $$\Delta t$$
What distance will you travel, constantly at the average velocity as defined in your post, over a time of $$\Delta t$$ ?

3. Aug 15, 2009

### demonelite123

for the first question, i would travel (vi)($$\Delta t$$)
for the second question, i would travel (average velocity)($$\Delta t$$)

is this right?

4. Aug 15, 2009

### Fightfish

No. Question one entails a constant acceleration starting with an initial velocity vi, and not a constant velocity.

5. Aug 16, 2009

### demonelite123

could you please show me how to derive the formula average velocity = (vf - vi) / 2 when acceleration is constant?

6. Aug 16, 2009