# Slow and steady wins the race

**Classical Mechanics**Level 3

Find the equation of cross-section of a circularly symmetrical bowl shaped racetrack such that the time of completing a lap in it is inversely proportional to the square of velocity of a race car by a constant of proportionality \(K\) .

If the equation is given by:

\(y=-\frac { a }{ b } \times \frac { { K }^{ c } }{ { \pi }^{ d }{ g }^{ e }{ x }^{ f } } \)

where \(g\) is the acceleration due to gravity and \(x\) is the distance from centre of the racetrack.

find,

\(\left| a \right| +\left| b \right| +\left| c \right| +\left| d \right| +\left| e \right| +\left| f \right| \)