Grade 12 Calculus

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

2x dx/dt + 2y dy/dt = 0

Substitute dx/dt = y to get

2y(x + dy/dt) = 0

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?


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