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

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

2. 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.

3. Originally Posted by walreinlim88
$\displaystyle v = \int{\frac{dv}{dt}\,dt}$

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

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

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

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

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

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

4. Originally Posted by Prove It
$\displaystyle v = \int{\frac{dv}{dt}\,dt}$

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

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

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

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

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

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

5. 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.

6. Originally Posted by mr fantastic
If that's the case, please post all your working and answers so that it can be reviewed.

is this answers correct?
thx

7. Originally Posted by walreinlim88

is this answers correct?
thx
I haven't checked every small detail but it looks OK.

8. 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

9. Originally Posted by mr fantastic
I haven't checked every small detail but it looks OK.
plz help me check asapTT ....thx

10. 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.