TheAlgorithms · autobotx343 · Jun 8, 2026 · Jun 8, 2026 · Jun 8, 2026 · Jun 9, 2026
diff --git a/physics/collisions.py b/physics/collisions.py
@@ -0,0 +1,142 @@
+"""
+Collision types and final velocities are central to physics.
+This module computes final velocities for inelastic and elastic collisions.
+It also classifies the collision type from initial and final velocities.
+
+Description: Collisions happen when two masses interact head-on.
+There are two types: inelastic and elastic. In inelastic collisions, the
+masses stick together and share one final velocity. In elastic collisions,
+momentum and kinetic energy are conserved, and masses rebound.
+Momentum is mass times velocity; kinetic energy is 1/2 mv^2.
+The collision type comes from comparing initial and final momentum and
+kinetic energy of the system.
+
+Reference: https://en.wikipedia.org/wiki/Collision
+"""
+
+
+def inelastic_collisions(
+    mass1: float, mass2: float, velocity1: float, velocity2: float
+) -> float:
+    """Calculate final velocity after a perfectly inelastic collision.
+
+    The two objects stick together and share a common final velocity.
+
+    Parameters:
+        mass1: Mass of the first object.
+        mass2: Mass of the second object.
+        velocity1: Initial velocity of the first object.
+        velocity2: Initial velocity of the second object.
+
+    Returns:
+        The final combined velocity of the two objects.
+
+    Complexity:
+        Time Complexity: O(1) - Constant execution time for basic arithmetic.
+        Space Complexity: O(1) - Constant memory allocation.
+
+    Examples:
+        >>> inelastic_collisions(2.0, 3.0, 5.0, 6.0)
+        5.6
+        >>> inelastic_collisions(9.0, 8.1, -3.2, 3.1)
+        -0.22
+    """
+    initial_momentum = (mass1 * velocity1) + (mass2 * velocity2)
+    total_mass = mass2 + mass1
+    final_velocity = round((initial_momentum / total_mass), 2)
+
+    return final_velocity
+
+
+def elastic_collisions(
+    mass1: float, mass2: float, velocity1: float, velocity2: float
+) -> str:
+    """Calculate final velocities after a perfectly elastic collision.
+
+    The collision is head-on and conserves both momentum and kinetic energy.
+
+    Parameters:
+        mass1: Mass of the first object.
+        mass2: Mass of the second object.
+        velocity1: Initial velocity of the first object.
+        velocity2: Initial velocity of the second object.
+
+    Returns:
+        A formatted string containing the final velocities of both objects.
+
+    Complexity:
+        Time Complexity: O(1) - Constant execution time for basic math loops.
+        Space Complexity: O(1) - Constant memory allocation for fixed-size lists.
+
+    Examples:
+        >>> elastic_collisions(1.0, 2.0, -3.0, -1.0)
+        '-0.34 ; -2.34'
+        >>> elastic_collisions(9.0, 8.1, -3.2, 3.1)
+        '2.76 ; -3.54'
+    """
+    com_velocity = inelastic_collisions(mass1, mass2, velocity1, velocity2)
+    initial_velocities = [velocity1, velocity2]
+    final_velocities = []
+
+    for vel in initial_velocities:
+        new_vel = -1 * (vel - com_velocity)
+        final_vel = com_velocity + new_vel
+        final_velocities.append(round(final_vel, 2))
+
+    return f"{final_velocities[0]} ; {final_velocities[1]}"
+
+
+def type_collision(
+    mass1: float,
+    mass2: float,
+    velocity_initial1: float,
+    velocity_initial2: float,
+    velocity_final1: float,
+    velocity_final2: float,
+) -> str:
+    """Determine the collision type from initial and final velocities.
+
+    Compares initial and final momentum and kinetic energy to classify the collision.
+
+    Parameters:
+        mass1: Mass of the first object.
+        mass2: Mass of the second object.
+        velocity_initial1: Initial velocity of the first object.
+        velocity_initial2: Initial velocity of the second object.
+        velocity_final1: Final velocity of the first object.
+        velocity_final2: Final velocity of the second object.
+
+    Returns:
+        A string describing the collision type.
+
+    Complexity:
+        Time Complexity: O(1) - Constant execution time for evaluation logic.
+        Space Complexity: O(1) - Constant memory allocation.
+
+    Examples:
+        >>> type_collision(1.0, 1.0, 2.0, 3.0, 2.0, 3.0)
+        'Perfectly Elastic Collision'
+        >>> type_collision(1.0, 1.0, 2.0, 3.0, 2.5, 2.5)
+        'Perfectly Inelastic Collision'
+        >>> type_collision(1.0, 1.0, 2.0, 3.0, 0.0, 0.0)
+        'Inelastic Collision'
+    """
+    momentum_initial = (mass1 * velocity_initial1) + (mass2 * velocity_initial2)
+    momentum_final = (mass1 * velocity_final1) + (mass2 * velocity_final2)
+    kinetic_initial = 0.5 * (
+        (mass1 * velocity_initial1**2) + (mass2 * velocity_initial2**2)
+    )
+    kinetic_final = 0.5 * ((mass1 * velocity_final1**2) + (mass2 * velocity_final2**2))
+
+    if kinetic_final == kinetic_initial and momentum_initial == momentum_final:
+        return "Perfectly Elastic Collision"
+    elif kinetic_final != kinetic_initial and momentum_initial == momentum_final:
+        return "Perfectly Inelastic Collision"
+    else:
+        return "Inelastic Collision"
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
diff --git a/physics/potential_energy.py b/physics/potential_energy.py
@@ -2,60 +2,110 @@
 
 """
 Finding the gravitational potential energy of an object with reference
-to the earth,by taking its mass and height above the ground as input
+to the earth,by taking its mass and height above the ground as input.
 
+Description : Potential energy is stored energy that depends on the
+position or configuration of objects within a force field. It can be
+released as kinetic energy when the objects move under that force.
 
-Description : Gravitational energy or gravitational potential energy
-is the potential energy a massive object has in relation to another
-massive object due to gravity. It is the potential energy associated
-with the gravitational field, which is released (converted into
-kinetic energy) when the objects fall towards each other.
-Gravitational potential energy increases when two objects
-are brought further apart.
+Gravitational potential energy is the energy an object has because of
+its position in a gravitational field. It is the potential energy a
+massive object has in relation to another massive object due to gravity.
+This energy is associated with the gravitational field and is released
+when the objects fall toward each other. Near the Earth's surface this
+potential energy is approximately proportional to mass, gravity, and
+height, so it is often written as U = mgh for a body close to Earth.
 
-For two pairwise interacting point particles, the gravitational
-potential energy U is given by
+Spring potential energy is the stored energy in an elastic spring when
+it is compressed or stretched from its rest length. For small deformations,
+it is proportional to the square of the displacement from equilibrium.
+
+For two point particles interacting pairwise, the gravitational potential
+energy U is given by
 U=-GMm/R
 where M and m are the masses of the two particles, R is the distance
 between them, and G is the gravitational constant.
-Close to the Earth's surface, the gravitational field is approximately
-constant, and the gravitational potential energy of an object reduces to
-U=mgh
-where m is the object's mass, g=GM/R² is the gravity of Earth, and h is
-the height of the object's center of mass above a chosen reference level.
 
 Reference : "https://en.m.wikipedia.org/wiki/Gravitational_energy"
 """
 
 
-def potential_energy(mass: float, height: float) -> float:
-    # function will accept mass and height as parameters and return potential energy
+def gravitational_potential_energy(mass: float, height: float) -> float:
     """
-    >>> potential_energy(10,10)
-    980.665
-    >>> potential_energy(0,5)
-    0.0
-    >>> potential_energy(8,0)
-    0.0
-    >>> potential_energy(10,5)
-    490.3325
-    >>> potential_energy(0,0)
-    0.0
-    >>> potential_energy(2,8)
-    156.9064
-    >>> potential_energy(20,100)
-    19613.3
+    Function calculates the gravitational potential energy of an object.
+
+    Parameters:
+        mass: Mass of the object
+        height: Height the object is at
+
+    Returns:
+        The value of energy in Joules
+
+    Complexity:
+        Time Complexity: O(1) - Constant execution time for evaluation logic.
+        Space Complexity: O(1) - Constant memory allocation.
+
+    Examples:
+        >>> gravitational_potential_energy(10,10)
+        980.665
+        >>> gravitational_potential_energy(0,5)
+        0.0
+        >>> gravitational_potential_energy(8,0)
+        0.0
+        >>> gravitational_potential_energy(10,5)
+        490.3325
+        >>> gravitational_potential_energy(0,0)
+        0.0
+        >>> gravitational_potential_energy(2,8)
+        156.9064
+        >>> gravitational_potential_energy(20,100)
+        19613.3
     """
     if mass < 0:
         # handling of negative values of mass
         raise ValueError("The mass of a body cannot be negative")
     if height < 0:
         # handling of negative values of height
         raise ValueError("The height above the ground cannot be negative")
+
     return mass * g * height
 
 
+def spring_potential_energy(spr_con: float, dspl: float) -> float:
+    """
+    Function calculates the spring potential energy of an object.
+
+    Parameters:
+        spr_con: The spring constant of a spring
+        dspl: The length of the displacement of the spring
+
+    Returns:
+        The value of energy in Joules
+
+    Complexity:
+        Time Complexity: O(1) - Constant execution time for evaluation logic.
+        Space Complexity: O(1) - Constant memory allocation.
+
+    Examples:
+        >>> spring_potential_energy(100,2)
+        200.0
+        >>> spring_potential_energy(10,0.5)
+        1.25
+        >>> spring_potential_energy(8,0)
+        0.0
+        >>> spring_potential_energy(14.6,8)
+        467.2
+        >>> spring_potential_energy(17,4.5)
+        172.125
+    """
+    if spr_con < 0:
+        raise ValueError("The values for spring_constant cannot be negative")
+
+    return 0.5 * spr_con * (dspl**2)
+
+
 if __name__ == "__main__":
     from doctest import testmod
 
-    testmod(name="potential_energy")
+    print(spring_potential_energy(17, 4.5))
+    testmod(name="gravitational_potential_energy")