Parametric Equation

[minneola24]

I just have a question on how they are getting the speed. What is the speed? Is it dy/dx?

I thought it was dy/dx and I got a different answer. Where are they getting theta = root 4 + 9/4 ?

 

[mmm4444bot]

Speed is the absolute value of velocity. The velocity is the rate at which distance traveled (s) changes with respect to time elapsed: ds/dt

With parametric equations, the velocity of the point is a function of how both the y-coordinate and the x-coordinate change, with respect to time.

v(t) = ds/dt = sqrt(dx/dt^2 + dy/dt^2)

(When motion is described parametrically, dy/dx is the rate at which the y-coordinate of the point changes with repsect to the x-coordinate, not with respect to time.)

If you understand that x' is dx/dt and y' is dy/dt, then you know from where sqrt(4 + 9/4) comes. :cool:

 

[HallsofIvy]

I would phrase that differently. Strictly speaking "absolute value" is defined only for numbers. If v is a vector then |v| is the "magnitude" or "length" of vector v. Of course, they have many of the same properties and uses which is why the same notation is used. (Or similar notation- most texts use double lines, || v|| to denote magnitude of a vector.)