Question

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.

Answer 1

Oh. Oh. Oh. I got this one.

Explanation:

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.