Question

The position of a particle is given by r(t)=(t+cos(t/2), -3sint).
What is the particles velocity vector when t=pi?

a)v=<0.5, -3>
b)v=<2, -3>
c)v=<0.5, 3>
d)v=<1.5, 3>
e)v=<2, 3>

Thank you so much!!

Answer 1

<b>v</b>(t) = d<b>r</b>/dt = (1-(1/2)sin(t/2),-3cost)

Now just plug in your t value:

<b>v</b>(π) = (1-(1/2)(1),-3(-1)) = (1/2,3)