Questions related to dv/dt = f(t).

**mr fantastic** · Apr 25th 2010, 08:30 PM

Originally Posted by walreinlim88

Integrate with respect to t to get v. Integrate v with respect to t to get x.

Please show what you have done and say where you are stuck if you need more help.

**Prove It** · Apr 25th 2010, 08:32 PM

Originally Posted by walreinlim88

$v = \int{\frac{dv}{dt}\,dt}$

$= \int{\sin{(\pi t)} - \sqrt{3}\cos{(\pi t)}\,dt}$

$= -\frac{1}{\pi}\cos{(\pi t)} - \frac{\sqrt{3}}{\pi}\sin{(\pi t)} + C_1$ .

$x = \int{v\,dt}$

$= \int{-\frac{1}{\pi}\cos{(\pi t)} - \frac{\sqrt{3}}{\pi}\sin{(\pi t)} + C_1\,dt}$

$= -\frac{1}{\pi ^2}\sin{(\pi t)} + \frac{\sqrt{3}}{\pi ^2}\cos{(\pi t)} + C_1 t + C_2$ .

Now if you have initial or boundary conditions, use them to find $C_1$ and $C_2$ .

**walreinlim88** · Apr 25th 2010, 09:02 PM

Originally Posted by Prove It

$v = \int{\frac{dv}{dt}\,dt}$

$= \int{\sin{(\pi t)} - \sqrt{3}\cos{(\pi t)}\,dt}$

$= -\frac{1}{\pi}\cos{(\pi t)} - \frac{\sqrt{3}}{\pi}\sin{(\pi t)} + C_1$ .

$x = \int{v\,dt}$

$= \int{-\frac{1}{\pi}\cos{(\pi t)} - \frac{\sqrt{3}}{\pi}\sin{(\pi t)} + C_1\,dt}$

$= -\frac{1}{\pi ^2}\sin{(\pi t)} + \frac{\sqrt{3}}{\pi ^2}\cos{(\pi t)} + C_1 t + C_2$ .

Now if you have initial or boundary conditions, use them to find $C_1$ and $C_2$ .

may i ask that : start from rest =v=0 when t=0... may u all provide answers 4 me? i actually have done this questions, but i has no confident to my answers, i just want to double check wif u all.. thx...

**mr fantastic** · Apr 26th 2010, 12:02 AM

Originally Posted by walreinlim88

may i ask that : start from rest =v=0 when t=0... may u all provide answers 4 me? i actually have done this questions, but i has no confident to my answers, i just want to double check wif u all.. thx...

If that's the case, please post all your working and answers so that it can be reviewed.

**walreinlim88** · Apr 26th 2010, 12:26 AM

Originally Posted by mr fantastic

If that's the case, please post all your working and answers so that it can be reviewed.

please......help me check...
is this answers correct?
thx

**mr fantastic** · Apr 26th 2010, 03:47 AM

Originally Posted by walreinlim88

please......help me check...
is this answers correct?
thx

I haven't checked every small detail but it looks OK.

**walreinlim88** · Apr 26th 2010, 04:05 AM

Originally Posted by mr fantastic

I haven't checked every small detail but it looks OK.

help me check every small detail..
i really not confident at all on my answers..
thx

**walreinlim88** · Apr 26th 2010, 08:55 AM

Originally Posted by mr fantastic

I haven't checked every small detail but it looks OK.

plz help me check asapTT ....thx

**mr fantastic** · Apr 26th 2010, 03:10 PM

Originally Posted by walreinlim88

plz help me check asapTT ....thx

I do not check every small detail - maybe someone else has the time. Clearly you know how to do the question so I don't see what your worry is.

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