What is the speed of the particle?

A particle moves with its position given by x=cos(4t) and y=sin(t), where positions are given in feet from the origin and time t is in seconds.

1 Answer
Nov 7, 2017

Oh. Oh. Oh. I got this one.


You can find the velocity by adding up the components, which you find by taking the first derivative of the x & y functions:

#dx/dt = -4sin(4t)#
#dy/dt = cos(t)#

So, your velocity is a vector with components as given above.

The speed is the magnitude of this vector, which can be found via the Pythagorean theorem:

#s = sqrt((-4sin(4t))^2 + cos^2(t))#

...there may be some clever way to simplify this further, but perhaps this will do.