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.
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.