A particle moves with its position given by x=cos6t and y=sint , where positions are given in feet from the origin and time t is in seconds.
Find the speed of the particle.
I took the derivative of each equation and then plugged it into the formula velocity=sqrt((dx/dt)^2+(dy/dt)^2).
I got ((-6sin6t)^2+cost^2)^(1/2)ft/s for the answer, but that is incorrect.
Am I going about this the wrong way?
There is nothing wrong with your answer. It's all depending on what form of expression you want.
You can see the velocity vector very clearly:
The restriction on displacement on either components are and
Velocities of each component are and
The object moves in harmonic motion following an elliptic path, where and . and are frequency and phase angle, respectively.
If you are interested in find time in relation to and , you have a lot of work to do. You must find the relation between and expressed in , where , which will involve ODE.
That's all, I have nothing more to give. Good luck!