Mathematics

Problem

A particle moves along the curve

y^{2}=4x

, where all coordinates are measured in meters and time

t

is measured in seconds. (a) When the particle is at the point

(9,6)

, its

x

-coordinate is increasing at

3\text{ m s}^{-1}

. Calculate

\dfrac{dy}{dt}

at that instant. (b) Determine the slope

\dfrac{dy}{dx}

of the curve at

(9,6)

and interpret its sign in terms of the particle’s motion. (c) Compute the instantaneous speed of the particle at that moment.