Expressions

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• Jul 16th 2006, 04:22 AM
malaygoel
Quote:

Originally Posted by nath_quam
i spotted an error we don't want to integrate answer should be 2x - 4

Which integration you are talking about
what should be 2x-4

Keep Smiiling
Malay
• Jul 16th 2006, 04:25 AM
nath_quam
For part i) of the question c original post, captain black has integrated to give a in terms of x we actually want to go the other way therefore answer should be 2x - 4
• Jul 16th 2006, 04:41 AM
malaygoel
Quote:

Originally Posted by nath_quam
For part i) of the question c original post, captain black has integrated to give a in terms of x we actually want to go the other way therefore answer should be 2x - 4

He used the expression a=dv/dt =dv/dx * dx/dt to calculate acceleration. He never used integration(he used integration only for calculating x in terms of t).

keep Smiling
Malay
• Jul 16th 2006, 04:42 AM
nath_quam
Well his answer is wrong do the question
• Jul 16th 2006, 04:55 AM
malaygoel
I don't know whether the question is wrong or not but I found that acc. is 2x -4 when v=1m/s

Keep Smiling
Malay
• Jul 16th 2006, 08:17 AM
topsquark
I have just reworked the whole question. The answers given for a) and b) in the original post are incorrect. As I mentioned before, the answers CaptainBlack came up with originally are correct.

-Dan
• Jul 16th 2006, 09:31 AM
CaptainBlack
Quote:

Originally Posted by nath_quam
i spotted an error we don't want to integrate answer should be 2x - 4

We obtain:

$\displaystyle a=\frac{dv}{dt}=\frac{d}{dt}(2-x)^2=2(2-x)(-1)\frac{dx}{dt}\ \ \ ..(1)$

By differentiation. Now we know that:

$\displaystyle v=(2-x)^2$

but $\displaystyle v=\frac{dx}{dt}$ which we may substitute back into (1) to get:

$\displaystyle a=\frac{dv}{dt}=2(2-x)(-1)\frac{dx}{dt}=-2(2-x)^3$.

RonL
• Jul 16th 2006, 04:52 PM
nath_quam
Quote:

Originally Posted by CaptainBlack
We obtain:

$\displaystyle a=\frac{dv}{dt}=2(2-x)(-1)\frac{dx}{dt}=-2(2-x)^3$.

RonL

i believe it should be to the power of 1 not 3
• Jul 16th 2006, 08:09 PM
CaptainBlack
Quote:

Originally Posted by nath_quam
i believe it should be to the power of 1 not 3

Then please show us your working, so we can see where I have gone wrong.

RonL
• Jul 16th 2006, 08:21 PM
nath_quam
Working
v = (2-x)^2
expanding gives
v = 4 - 4x + x^2
a= dv/dx = 2x -4
or
v = (2-x)^2
a = dv/dx = using d/dx[f(x)^n] = f'(x)n[f(x)]^(n-1)
a = ((-1)(2))(2-x)^(2-1)
a = -2(2-x)
a = 2x - 4
• Jul 16th 2006, 08:24 PM
malaygoel
Quote:

Originally Posted by nath_quam
v = (2-x)^2
expanding gives
v = 4 - 4x + x^2
a= dv/dx = 2x -4
or
v = (2-x)^2
a = dv/dx = using d/dx[f(x)^n] = f'(x)n[f(x)]^(n-1)
a = ((-1)(2))(2-x)^(2-1)
a = -2(2-x)
a = 2x - 4

a is not dv/dx.
a is dv/dt

Malay
• Jul 16th 2006, 08:29 PM
nath_quam
ah true i'll get back to you i have to think

ummm..... isn't a = the derivative of v
• Jul 17th 2006, 03:31 AM
nath_quam
Just Quickly
Quote:

Originally Posted by CaptainBlack
Like this:

$\displaystyle v=\frac{dx}{dt}=(2-x)^2$

which is a differential equation of variables seperable type, and so:

$\displaystyle \int\frac{dx}{(2-x)^2}=\int dt$,

which may be integrated to give:

$\displaystyle \frac{1}{2-x}=t+const$

and as $\displaystyle x=0$ when $\displaystyle t=0,\ const=1/2$, then rearranging:

$\displaystyle x=\frac{4t}{2t+1}$

RonL

I believe the constant is -1/2 making the answer the same

why can't this part

$\displaystyle \frac{1}{2-x}=t+const$

be

$\displaystyle \frac{1}{2-x}+const=t$
• Jul 17th 2006, 03:55 AM
topsquark
Quote:

Originally Posted by nath_quam
ah true i'll get back to you i have to think

ummm..... isn't a = the derivative of v

As malaygoel stated, a is the time derivative of v.

As to the previous post, yes the constant can be on either side of the equation, but they would be different constants...

-Dan
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