## Need help with acceleration/time physics...

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Posts: 28
Joined: 2006.12
Post: #16
Skorche Wrote:Once again, while you didn't use any calculus, the formula d = ut + 1/2atÂ² is derived using ideas from calculus.

But it isn't just the area of a trapezoid, it is the area of a right trapezoid which is essentially a rectangle and a triangle. I don't see where calculus comes in here (if this is calculus then I can claim I started learning calculus in 3rd grade ).
Sage
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Post: #17
It's because you are relating the area under a curve on the velocity graph to the distance that makes it calculus. Calculus was developed partly to solve problems just like this.

Yes, finding the area of a rectangle and a triangle is easy, but would you have ever guessed that doing so relates the velocity to the distance? Unless you were told so, I'd suspect that you wouldn't have.

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Post: #18
unknown Wrote:yeah but the idea of v-bar, average time for an entire journey is not derived from calculus, neithe was anything in my post. (the one that I didnt make a stupid mistake in that is)

The fact that you use an average velocity over an infitesimal period of time to approximate a function is calculus. When you use the "average" velocity formula in a numerical integrator, it becomes trapezoidal integration.
Sage
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Joined: 2005.07
Post: #19
no its not the average over âˆ‚t, its the mean of two numbers, u and v, initial velocity and current velocity (this applies only to a constant acceleration).

If you look at http://en.wikipedia.org/wiki/Equations_o...equation_2

it stating the equation v bar = s/t (thought it calls v bar average velocity), which for a constant acceleration alone = (u+v)/2.
This was all known before calculus techniques and does not make any assumptions about graphs or areas under graphs.

as I showed in a previous post the two equations
v = u + at
s = 1/2 * (u + v) * t

are both derived from basic mathematics and the resulting formula for t in terms of s and a was derived from simple algebraic manipulation.

so you dont need calculus for somthing this simple!

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Posts: 28
Joined: 2006.12
Post: #20
I see where I was wrong. However, I think Unknown is also right that you are looking at the average velocity which has nothing to do with the graph of the velocity.

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