Math Help - [SOLVED] Position and Velocity vector??

1. [SOLVED] Position and Velocity vector??

Find the position and velocity vectors if the acceleration is
$A(t)= (cost)i -(tsint)k$
and the initial position and velocity vectors are $R(0)=i-2j+k$ and $V(0)=2i+3k$ respectively.

Any help is appriciated, bla bla..

2. Originally Posted by Lafexlos
Find the position and velocity vectors if the acceleration is
$A(t)= (cost)i -(tsint)k$
and the initial position and velocity vectors are $R(0)=i-2j+k$ and $V(0)=2i+3k$ respectively.

Any help is appriciated, bla bla..
Show us what work you have done so far, we can help you from there. bla bla

3. Unfortunately, couldn't do anything on it.
It looks gonna take integral of acceleration and put zero and gonna find velocity but i can not take the integral of vector. :S

is it same as normal integral and put i , j , k? or does it exist something like integral of vector?

4. Originally Posted by Lafexlos
Find the position and velocity vectors if the acceleration is
$A(t)= (cost)i -(tsint)k$
and the initial position and velocity vectors are $R(0)=i-2j+k$ and $V(0)=2i+3k$ respectively.

Any help is appriciated, bla bla..
To integrate a vector all you do is integrate the individual components.

For example, a vector such as $t^2 i + 3t j - 5k$, differentiated with respect to $t$ would be, $2t i + 3 j$.

Hope this helps.

Edit: The same rules for integration apply.

5. Originally Posted by craig
Show us what work you have done so far, we can help you from there. bla bla
$a(t) = (\cos{t})i - (t\sin{t})j$

i component ...

you should already know the antiderivative of $\cos{t}$.

j component ...

you'll have to use integration by parts to find the antiderivative of $t\sin{t}$. give it a go.

6. So, $\int A(t)= (sint) i+ (c) j + (sint-tcost) k + C$
i think, now i should put zeros instead of $t$ but when put zero for $i$ component i get $0i$ but instant velocity has $i$ component. Does it mean that $C$ has $i$ component?
Bah. Really confused but understand the logic. =) Thx for helps.

7. You have forgotten the "constants of integration" for each component.

8. Ok. I see.
So it'll be $(sint + C)i$ instead of $(sint)i + C$. Now everything is complete.