Tim Grade 12 Calculus Student Related Rates Problem A particle moves around the circle x^{2} + y^{2} = 1 with an xvelocity component dx/dt = y
Hi Tim, Both x and y are functions of t so you can differentiate the expression x^{2} + y^{2} = 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 (x_{0},y_{0}). Draw a vector from P in the xdirection with length y_{0} (xvelocity component). Draw a vector from P in the ydirection with length x_{0} (yvelocity component). Graphically add these vectors to get the velocity vector. In which direction is the particle moving?
Cheers,
