Related Rates

posted by .

A particle moves along a path described by y=x^2. At what point along the curve are x and y changing at the same rate? Find this rate if at time t we have x=sin t and y= sin^2t.

I solved the first part and got (1/2, 1/4), but I have no idea how to tackle the second part. Help is much appreciated.

  • Related Rates -

    dy/dt = dy/dx * dx/dt
    but
    dy/dx = 2x
    so
    dy/dt = 2 x dx/dt
    so when 2 x = 1 (when the slope = 1 of course)

    x = 1/2 then y = 1/4

    x = sin t
    when is sin t = 1/2
    when t = 30 degrees or pi/6 radians
    dx/dt = cos t = cos 30 = (sqrt 3 )/ 2
    dy/dt = 2 sin t cos t = 2(1/2)(sqrt 3/2) sure enough

  • Related Rates -

    Thank you very much. I understand it now. :-)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus (related rates)

    A particle moves in the plane along the curve y=xln(x). At what rate is the distance from the origin increasing at the moment its x-coordinate is 2 cm and its x-coordinate is increasing at a rate of 17 cm/sec?
  2. college calculus

    1) each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square is 16 cm^2?
  3. calculus

    Can someone tell me how to do this type of problem?
  4. math

    a particle moves along the curve y= sqrt 1+x cubed. As it reaches the point (2,3) the y-corrdinate is increasing at a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant?
  5. Calculus

    A particle moves along the curve y = sqr(1+x^3). As it reaches the point (2,3), the y-coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at that instant.
  6. Calculus

    1. The radius of a sphere is expanding at a rate of 14 in/min. a) Determine the rate at which the volume is changing when the radius is 8 in. b) Determine the rate at which the surface area is changing when the radius is 8 in. 2. A …
  7. Calculus

    1. The radius of a sphere is expanding at a rate of 14 in/min. a) Determine the rate at which the volume is changing when the radius is 8 in. b) Determine the rate at which the surface area is changing when the radius is 8 in. 2. A …
  8. calc

    A particle moves along the curve below. y = sqrt(8 + x^3) As it reaches the point (2, 4), the y-coordinate is increasing at a rate of 5 cm/s. How fast is the x-coordinate of the point changing at that instant?
  9. Calculus

    A particle moves along the curve y = 3x2 + 1 in such a way that the y value is increasing at the rate of 3 units per second. At what rate is x changing when x = 2?
  10. Calculus

    A particle moves along the curve y=lnx so that its abscissa is increasing at a rate of 2 units per second. At what rate is the particle moving away from the origin as it passes through the point (1,e)?

More Similar Questions