Question

A particle is moving along the curve y= 5 \sqrt{4 x + 1}. As the particle passes through the point (2, 15), 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.

Answer 1

$y = 5 \sqrt{4x + 1}$

$y = 5(2 x^{ \frac{1}{2} } + 1)$

$y = 5(2 x^{ \frac{1}{2} }) + 5(1)$

$y = 10 x^{ \frac{1}{2} } + 5$