Question

Calculate the trajectory position vector, when given the velocity vector and the initial position.

Answer 1

to early for this

Answer 2

Since velocity is:

\[\vec v = \frac{d \vec r}{dt}\]

Integrate both sides by dt:

\[\int \vec v dt = \int \frac{d \vec r}{dt} dt\]
By fundamental theorem of calculus the right hand side's derivative and integral cancel out leaving you with just this:

\[\int \vec v dt = \vec r\]

Once you solve this, you'll have a constant of integration that you can solve for by plugging in t=0 and \(\vec v(0)\) to solve for it, and that'll be it. Give it your best shot and show me what you do if you get stuck.

Answer 3

Maybe I confused you with all this fancy symbols nonsense haha. Really all I'm saying is integrate your velocity to get the position vector.

Answer 4

yeah i got thanks.