# Deriving a common formula

#### Matt1234

1. The problem statement, all variables and given/known data

See the attachment please.

3. The attempt at a solution

I know the v1 x delta (t) is for the rectangle,
I dont see how the second part works? I dont understand why the t^2 and how a replaces the area formula i have written.

Thanks for your help, its my first day of class today, and its been a while since i was last in a physics / math class.

EDIT: I added a formula sheet we were given, sorry i just dont see the relationship right now..

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#### CompuChip

Homework Helper
You can replace $\Delta v = v_2 - v_1$ by the acceleration a. In the picture, the acceleration is the slope of the line, algebraically it is given by
$$a = \frac{\Delta v}{\Delta t}$$.

So just write down the area of the triangle and do the substitution.

#### wavingerwin

from the second equation on the formula sheet,
a=$$\Delta$$v/$$\Delta$$t
a=(vf-vi)/t

from the graph, d=vit+$$\frac{1}{2}$$(vf-vi)*t
therefore, d=vit+$$\frac{1}{2}$$at2
(since vf-vi=at)

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