How fast is the distance from the particle to the origin changing at this instant?

Question

A particle is moving along the curve y = Square root of (x). As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant?

Answer 1

The distance from the origin be S and the formula for that is 

S=square root of X²+Y²

 

The given function is Y=square root of X

 

plug in the S function for Y , you get S=square root of X²+X

 

Find the derivative WRT time 

dS/dt=1/2(x²+X)^-1/2(2X+1)dX/dt

 

plug in the value of X=4 and dX/dt as 3 you get dS/dt=27/4square rootof5  cm/s