Related Rates Problem

A particle moves around the circle x² + y² = 1 with an x-velocity component dx/dt = y

1. Find dy/dt

2. Does the particle travel clockwise or counterclockwise around the circle? Why?

Hi Tim,

Both x and y are functions of t so you can differentiate the expression x² + y² = 1 to get

Substitute dx/dt = y to get

Hence if y is not zero then dy/dt = -x.

Now draw a circle with center at the origin and mark some point P on it. Suppose its coordinates are (x₀,y₀). Draw a vector from P in the x-direction with length y₀ (x-velocity component). Draw a vector from P in the y-direction with length -x₀ (y-velocity component). Graphically add these vectors to get the velocity vector. In which direction is the particle moving?

Cheers,
Harley