Add relativistic kinetic energy

physics/relativistic_kinetic_energy.py

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+"""
+Find the relativistic kinetic energy of a particle, given its rest mass and velocity.
+
+Description: In special relativity, the kinetic energy of a particle is the extra
+energy it has due to its motion beyond the energy associated with its rest mass.
+It is defined as the difference between the total relativistic energy and the rest
+energy of the particle. After a force does work to accelerate a particle from rest
+to some high speed comparable to the speed of light, the particle carries this
+relativistic kinetic energy as long as its speed stays the same. The same amount of
+energy must be removed (for example, by an opposite force) to slow the particle
+back down to rest. Formally, relativistic kinetic energy appears in the relativistic
+energy momentum relation and depends on the Lorentz factor, which encodes how time
+and space change at high speeds.
+
+In relativistic mechanics, the kinetic energy K of a particle with rest mass m
+moving at speed v is
+
+    K = (y - 1) m c^2,
+
+where c is the speed of light in vacuum and
+
+    y = 1 / sqrt(1 - v^2 / c^2)
+
+is the Lorentz factor. At speeds much smaller than c, this expression reduces to the
+classical formula K ≈ (1/2) m v^2, so the relativistic result agrees with Newtonian
+kinetic energy in the low velocity limit.The standard unit of kinetic energy is the
+joule, while the English unit of kinetic energy is the foot-pound.
+
+Reference : https://en.wikipedia.org/wiki/Kinetic_energy
+"""
+
+from math import sqrt
+
+from scipy.constants import c  # speed of light in vacuum (299792458 m/s)
+
+
+def relativistic_kinetic_energy(mass: float, velocity: float) -> float:
+    """
+    Calculate relativistic kinetic energy.
+    mass --- kg
+    velocity ---- m/s
+    K.E ---- j
+
+    >>> relativistic_kinetic_energy(10,10)
+    598.6912157608277
+    >>> relativistic_kinetic_energy(40,200000)
+    800000266962.5057
+    >>> relativistic_kinetic_energy(50,100000)
+    250000021062.11475
+    >>> relativistic_kinetic_energy(0,0)
+    0.0
+    >>> relativistic_kinetic_energy(100,0)
+    0.0
+
+    """
+
+    if mass < 0:
+        raise ValueError("The mass of a body cannot be negative")
+    else:
+        gamma = 1 / sqrt(1 - (velocity**2 / c**2))
+        return (gamma - 1) * mass * c**2
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()