The Smaller the Curvature in a Bend of a Road $y = \frac { 1 } { 3 } x ^ { 3 } ( x \text { and } y \text { are measured in miles) can safely go } 25 \text { miles per hour at }$

Multiple Choice

The smaller the curvature in a bend of a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car Moving on the path $y = \frac { 1 } { 3 } x ^ { 3 } ( x \text { and } y \text { are measured in miles) can safely go } 25 \text { miles per hour at }$ $\left( 1 , \frac { 1 } { 3 } \right)$ . How fast can it go at $\left( \frac { 5 } { 2 } , \frac { 125 } { 24 } \right)$ ? Round your answer to two decimal places.

A) $259.31 \mathrm { mi } / \mathrm { h }$
B) $149.71 \mathrm { mi } / \mathrm { h }$
C) $119.77 \mathrm { mi } / \mathrm { h }$
D) $75.30 \mathrm { mi } / \mathrm { h }$
E) $299.42 \mathrm { mi } / \mathrm { h }$