Question

A particle is moving along the curve y=3 sqrt 2x+5 . As the particle passes through the point (2,9), its -coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant

Answer 1

Differentiating the equation wrt time
dy/dt=3dx/dt (2x+5)^(-1/2)

As dy/dt=4, we can put x=2 for the given point and find that dx/dt=4.

distance from origin R= sqrt (x^2 + y^2)
We have to find dR/dt
=
[xdx/dt + ydy/dt]/[sqrt D]

Knowing x,y, dx/dt and dy/dt at that point we can evaluate the answer