Hello I was trying to find the proof of the formula
x = x0 + v0t +.5at^2
were the zeros are subscripts
My text book dosen't explain it that well.
ok well
it involves the formula for
average velocity
aver velocity = 2^-1(v0 + v)
were the zero is a subscript and this is just because if there is constant acceleration than the velocity average is between the inital and final I understand this
ok it also involves using this formula
x = x0 + average velocity(t)
which I understand the proof of how to get this formula were the zero is a subscript
ok so in my book it shwos the proof like so
x = x0 + average velocity(t)
were the zero is a subscript
then you plug in that other formula and get this
x = x0 + (2^-1(v0 +v))t
were the zeros are subscripts
ok this is were I get lost
then next step in my text book shows this
x = x0 + (2^-1(v0 + v0 at))t
were zeros are subscripts
ok were did the extra v0 come from?
were did the at come from?
then of course the next line
x = x0 + v0t + .5at^2
I was hopeing somebody could explain to me this proof
THANK YOU!
I FIGUERED IT OUT THANKS
Ok, good. It is kind of artificial because you are doing calculus without calculus.
Sure, let's go step by step and explain the proof of the formula.
Starting with:
x = x0 + average velocity(t)
This equation represents the position (x) of an object at time (t) in terms of its initial position (x0) and average velocity.
Now, we substitute the formula for average velocity:
x = x0 + (2^-1(v0 + v))t
Here, we're using 2^-1 as a way to represent the average between v0 (initial velocity) and v (final velocity).
The next step in your textbook shows:
x = x0 + (2^-1(v0 + v0 at))t
Here, we're introducing acceleration (a) into the equation. The extra v0 comes from the fact that we're considering the average velocity over the time period (t), and the object starts with an initial velocity of v0. So, we add v0 to the average velocity term (2^-1(v0 + v)) and obtain v0 + v0, which simplifies to 2v0.
As for the at term, it comes from the concept of constant acceleration. When an object experiences constant acceleration, its final velocity (v) is given by v = v0 + at, where a is the acceleration and t is the time elapsed. We can substitute this expression for v in our equation.
Combining these ideas, we get:
x = x0 + (2^-1(v0 + v0 at))t
x = x0 + v0t + v0at
Finally, by factoring out v0 from the last two terms, we obtain the familiar formula:
x = x0 + v0t + 0.5at^2
I hope this explanation clarifies the derivation of the formula for you. Let me know if you have any further questions!