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- Thread starter mathkid3
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- Jan 26, 2012

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Acceleration

What equation did you use to solve for "a"? I suggest using ${v_f}^2={v_i}^2+2ad$

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(1) $\displaystyle \Delta v=v_f-v_i=at$

(2) $\displaystyle \Delta x=\frac{1}{2}at^2+v_it$

From (1), we may state:

$\displaystyle t=\frac{v_f-v_i}{a}$ and substituting into (2) we find:

$\displaystyle \Delta x=\frac{1}{2}a\left(\frac{v_f-v_i}{a} \right)^2+v_i\left(\frac{v_f-v_i}{a} \right)$

Multiplying through by $2a$ we obtain:

$\displaystyle 2a\Delta x=v_f^2-v_i^2$

This is equivalent to the relation cited by

$\displaystyle a=\frac{v_f^2-v_i^2}{2\Delta x}$

Now plug-n-chug!

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$v_f$ is the final velocity, and since the car came to a stop, this is $0\,\dfrac{\text{m}}{\text{s}}$

$v_i$ is the initial velocity which is given as $100\,\dfrac{\text{m}}{\text{s}}$

So, plug in those values (along with the units, it is important in a physics course to get used to carrying the units too) and what do you get?