apple_pi
If a car travelling at vm/s takes X meters to stop, what would the stopping distance be if it was travelling at 3vm/s (assume stopping force is equal)



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apple_pi
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I remember doing this in class, but forgot which equation to use

lgbasallote
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hmm could it be \[V_2 ^2 = V_1 + 2as\]
where s is the distance

lgbasallote
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correction.. \[V_2 ^2 = V_1^2 + 2as\]

apple_pi
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V is velocity?
a is acceleration?
s is displacement?

lgbasallote
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yup

apple_pi
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Oh... yeah so that's the same one I have here as
v^2=u^2+2as

lgbasallote
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yep same shiz

lgbasallote
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so first find the acceleration using
v = 0
u = v
s = X

apple_pi
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0=v^2+2aX... what is a?

lgbasallote
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you solve for it

lgbasallote
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isolate a

apple_pi
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a=v^2/2X

lgbasallote
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right

lgbasallote
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now use
v^2 = u^2 + 2as again
this time use:
v = 0
u = 3v
a = v^2/2X

lgbasallote
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then solve for s

apple_pi
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starting with 0=9v^2+2aX
9v^2/2a=X
9v^2/2(v^2/2X)=X
9X=X
now what?

lgbasallote
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no...

lgbasallote
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it's not 2aX

lgbasallote
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it's 2as

lgbasallote
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X is just for the first situation

apple_pi
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oh i see

lgbasallote
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\[0 = 9v^2 + 2as\]
\[9v^2 = 2as\]
\[\frac{9v^2}{2a} = s\]
\[\frac{9v^2}{2(\frac{v^2}{2X})} = s\]
\[\implies \frac{9v^2}{\frac{v^2}{X}} = s\]
\[\implies 9X= s\]

apple_pi
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Oh. THank You!

lgbasallote
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welcome