Average velocity question

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.

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 $$\Delta t$$ ?

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 $$\Delta t$$ ?

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

is this right?

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

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

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

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

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.

It may help your understanding if you sketch a v/t graph.Find the area underneath the graph to get the distance travelled and use, average velocity = distance/ time

It may help your understanding if you sketch a v/t graph.Find the area underneath the graph to get the distance travelled and use, average velocity = distance/ time

thanks! i got it now!