Conservation of momentum and energy(part 1)

According to the conservation of momentum, when two objects collide, their net momentum before collision & after collision is equal.

Imagine two object of masses m_1 & m_2 in motion with initial velocities of u_1 & u_2 respectively. After their collision, they have velocities of v_1 & v_2 (mass is constant). Applying the conservation of momentum, we get,


Likewise we can form such an equation for the conservation of kinetic energy that says,


(We know that E_k=\dfrac{1}{2}mv^2)

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(part 2,3&4 is coming soon)

thank you ArnabZ for editing. Actually I have confusions in writing code for this fonts.