The path of a particle moving in the plane is defined parametrically as a function of time t by x=sin(2t) and y=cos(5t). Find the speed of the particle when t=2.

Question

kainui · Answer

So what's your best guess? If you can't give me a guess, explain to me where you're having trouble understanding.

anonymous · Answer

Do I find dy/dx and plug 2 in?

kainui · Answer

No, y and x are both functions of t. What you have is a vector,

s(t)=<sin2t, cos5t>

and you need to differentiate for the velocity and then find the length of the velocity vector with the pythagorean theorem since speed is just the magnitude of the velocity, and plug in 2 to find the exact speed at that time.

anonymous · Answer

@iambatman

anonymous · Answer

I only want to verify my answer. Please tell me the right answer. You don't need to show your work.