Question

A particle is moving along the curve y=4sqrt(4x+1) . As the particle passes through the point (2,12), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

Thanks !!!

Answer 1

y= 4sqrt(4x+1)

dy/dt= 4*1/2*1/sqrt(4x+1)*4dx/dt

you are given dx/dt, solve for dy/dt

now, since r=sqrt(x^2+y^2)
dr/dt= 1/2 *1/sqrt(x^2+y^2)* (2xdx/dt+2ydy/dt)

solve for dr/dt