PROBLEM STATEMENT

Subway trains can move people quickly from one station to the next. It is known that the distance 
between two consecutive stations is length meters. For safety, the train can't move faster than 
maxVelocity meters/sec. For comfort, the absolute acceleration can't be larger than 
maxAcceleration meters/sec^2. The train starts with velocity 0 meters/sec, and it must stop at the 
next station (i.e., arrive there with a velocity of 0 meters/sec). Return the minimal possible 
time to get to the next station.


DEFINITION
Class:Subway2
Method:minTime
Parameters:int, int, int
Returns:double
Method signature:double minTime(int length, int maxAcceleration, int maxVelocity)


NOTES
-Your return value must be accurate to within an absolute or relative tolerance of 1E-9.
-If the train's speed at time 0 is v0 and the acceleration is always a, then at time t the speed 
will be (v0 + t * a) and the train will be (v0 * t + 0.5 * a * t^2) away.


CONSTRAINTS
-length, maxAcceleration and maxVelocity will each be between 1 and 1000, inclusive.


EXAMPLES

0)
1
2
10

Returns: 1.4142135623730951

maxVelocity is very large. So the train can keep speeding up until it reaches position 0.5.

1)
1
1
1

Returns: 2.0



2)
10
1
1

Returns: 11.0

The train reaches its maximum velocity after 1 second, while traveling 0.5 meters.  It then 
travels the next 9 meters in 9 seconds, and takes 1 second to decelerate to 0 m/s while covering 
the final 0.5 meters.

3)
1
10
1

Returns: 1.1



4)
778
887
384

Returns: 2.458961621570838

5)
336
794
916

Returns: 1.301036207838119

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