# A calculus problem by Ραμών Αδάλια

Calculus Level pending

Given the functions

$$f\left( t \right) =\frac { 1 }{ 3 } { t }^{ 3 }$$

$$g\left( t \right) =\frac { \sqrt { 5 } }{ \sqrt { 2 } } { t }^{ 2 }$$

$$h\left( t \right) =5t$$

where $$t$$ represents the time in seconds, and $$f\left( t \right)$$, $$g\left( t \right)$$ and $$h\left( t \right)$$ the position in the 3 distinct axis, find the distance traveled in the first 5 seconds, $$a$$. Input your answer as $$\left\lfloor a \right\rfloor$$.

Notes: By distance traveled, we understand the length of the arc of the trajectory, not the displacement between two points. The initial time is 0 seconds. Thus, the interval of time is from 0 to 5 seconds. Units are trivial.

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