Grade 12 Calculus
Related Rates Problem
A particle moves around the circle x2 + y2 = 1 with an x-velocity component dx/dt = y
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?