Braking distance d1 is the distance a vehicle will go from the point when it brakes to when it comes to a complete stop. It depends on the original speed v and on the coefficient of friction mu between the tires and the road surface.

Braking distance is just one of two principal components of the total stopping distance. The other component is the reaction distance, which is the product of the speed and the perception-reaction time of the driver. We can just assume that the reaction time is constant and equal to 1 second.

The kinetic energy E can be found using the formula 0.5*m*v**2, the work W given by braking is mu*m*g*d1. Finding E and W gives the braking distance: d1 = v*v / 2*mu*g where g is the gravity of Earth and m the vehicle's mass.

So, to complete this challenge, there are two tasks you need to complete.

1. Calculate the total stopping distance in meters given v, mu (and the reaction time t = 1).
   dist(v, mu) -> d = total stopping distance

2. Calculate v in km per hour knowing d in meters and mu. The reaction time is still t = 1.
   speed(d, mu) -> v such that dist(v, mu) = d

Examples

1. dist(100, 0.7) -> 83.9598760937531

2. speed(83.9598760937531, 0.7) -> 100.0

Tests

dist(144, 0.3)
dist(92, 0.5)

speed(159, 0.8)
speed(153, 0.7)

Good luck!

This challenge comes from g964 on CodeWars. Thank you to CodeWars, who has licensed redistribution of this challenge under the 2-Clause BSD License!

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