Vector, Parametrics help

• March 30th 2010, 07:00 PM
Vector, Parametrics help
A particle moves in the plane in such a manner that its coordinates at time t are:
x=3cos((pi/4)t)
y=5sin((pi/4)t)

a)Find the length of the velocity vector at t=3
b)find the x- and y- components of acceleration of the particle at t=3
c)Find a single equation in x and y for the path of the particle

Please explain to me how to do this or possible phrase these questions better, thank you.
• March 30th 2010, 07:23 PM
skeeter
Quote:

A particle moves in the plane in such a manner that its coordinates at time t are:
x=3cos((pi/4)t)
y=5sin((pi/4)t)

a)Find the length of the velocity vector at t=3
b)find the x- and y- components of acceleration of the particle at t=3
c)Find a single equation in x and y for the path of the particle

Please explain to me how to do this or possible phrase these questions better, thank you.

a) $|v| = \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2}$

... evaluated at t = 3

b) $a_x = \frac{d^2x}{dt^2}$

$a_y = \frac{d^2y}{dt^2}$

... both evaluated at t = 3

c) $x^2 = 9\cos^2\left(\frac{\pi t}{4}\right)$

$\frac{x^2}{9} = \cos^2\left(\frac{\pi t}{4}\right)$

$y^2 = 25\sin^2\left(\frac{\pi t}{4}\right)$

$\frac{y^2}{25} = \sin^2\left(\frac{\pi t}{4}\right)$

$\frac{x^2}{9} + \frac{y^2}{25} = \cos^2\left(\frac{\pi t}{4}\right) + \sin^2\left(\frac{\pi t}{4}\right)
$

finish it ...