Question

(a) Find the position vector of a particle that has the given acceleration and the specified initial velocity and position.
a(t) = 18t i + sin t j + cos 2t k

I got (9/2 t^2 +t)i+(t-sint+1)j+(1/4 -1/4 cos 2t)k

Answer 1

Where are the given initial values?

Answer 2

v(0) = i, r(0) = j

Answer 3

@zepdrix

Answer 4

\(v(t) = (9t^2 + c_1)\hat{i} + (-\cos t +c_2)\hat{j}+(\frac{1}{2}\sin 2t + c_3)\hat{k}\)

yes?

Answer 5

are you there?

Answer 6

/???

Answer 7

no?

Answer 8

is that the final answer???:S

Answer 9

no, that's v(t). you know v(0) = i so plug in 0 for t and see what the c's are.

\[v(0) = (9(0)^2 + c_1)\hat{i}+(-\cos (0) + c_2)\hat{j}+(\frac{1}{2}\sin(2\cdot 0)+c_3)\hat{k}=\hat{i}\]
so \(c_1=1, c_2=1 \text{ and }c_3 = 0\)

now integrate again and use the fact that \( r(0) = \hat{j}\) to find out the variables of integration. then you'll have the required position vector.