# What is the speed of the particle?

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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.

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.

#### Explanation:

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

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:

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