Homework Help: Vector calculus

1. Feb 12, 2012

danny_manny

1. The problem statement, all variables and given/known data

Use the given information to find the position and velocity
vectors of the particle.

a(t) = −cos t i − sin t j; v(0) = i; r(0) = j

2. Relevant equations

3. The attempt at a solution
Ok first step integrate a(t).

which i get to be
-sin(t)i +cos(t)j + c

now using the initial condition v(0) = i
i get v(t) = 1-sin(t)i +cos(t)j

now integrate v(t)

= (cos(t)+t)i +sin(t)j
using initial condition r(0) = j
r(t) = (cos(t) + t)i + (sin(t)+1)j

they are my two answers in bold but the back of my book has different answers and i don't know whats going wrong.

Thanks for the assistance

2. Feb 12, 2012

SammyS

Staff Emeritus
Your v(t) is incorrect. It gives you that v(0) = 1 + j. That's neither a vector nor a scalar. You can't add a vector & a scalar.

The constant, c, you have after integrating a(t) is a vector constant, c.

3. Feb 12, 2012

danny_manny

so the vector constant should be equal to i no?

4. Feb 12, 2012

SammyS

Staff Emeritus
No, although I see that you may have meant to have v(t) = (1-sin(t))i + cos(t)j. But that still ignores the fact that cos(0) = 1, not zero.

5. Feb 12, 2012

danny_manny

(1-sin(t))i+(cos(t)+1)j ?

in the book however the answer is given
(1-sin(t))i+(cos(t)-1)j

I don't know where I'm going wrong.
Thanks again.

6. Feb 12, 2012

SammyS

Staff Emeritus
cos(0) - 1 = 1 - 1 =0

7. Feb 12, 2012

danny_manny

Sorry Sammy I'm still lost :(

8. Feb 12, 2012

vela

Staff Emeritus

9. Feb 12, 2012

danny_manny

v(0) = -sin(0)i +cos(0)t + c
= 0i+1j+c

10. Feb 12, 2012

vela

Staff Emeritus
I don't see how you solved for c.

11. Feb 12, 2012

danny_manny

That's the part I'm stuck at do i set the lhs equal to zero?

12. Feb 12, 2012

vela

Staff Emeritus
What do the initial conditions given in the problem statement say?

13. Feb 12, 2012

danny_manny

oh I see, thanks.