After collision velocity of first body equal to velocity of another body

Collision and Elasticity:

When two particles collide, they can either collide elastically or inelastically. In an elastic collision, both the momentum and kinetic energy of the system are conserved. This means that after the collision, the particles continue to move with the same total momentum and kinetic energy as before the collision.

Elastic Collision Equation:

In an elastic collision between two particles, the conservation of momentum and kinetic energy can be expressed using the following equations:

Momentum Conservation:
m1u1 + m2u2 = m1v1 + m2v2

where m1 and m2 are the masses of the two particles, u1 and u2 are their initial velocities, and v1 and v2 are their final velocities.

Kinetic Energy Conservation:
(1/2)m1u1^2 + (1/2)m2u2^2 = (1/2)m1v1^2 + (1/2)m2v2^2

where m1 and m2 are the masses of the two particles, u1 and u2 are their initial velocities, and v1 and v2 are their final velocities.

Elastic Collision Example:

Let's consider a particle of mass m1 moving with initial velocity u1 colliding elastically with another particle of mass m2 initially at rest (u2 = 0). After the collision, the first particle continues to move with final velocity v1, and the second particle moves with final velocity v2.

Using the equations of momentum and kinetic energy conservation, we can solve for the final velocities:

Momentum Conservation:
m1u1 + m2u2 = m1v1 + m2v2
m1u1 = m1v1 + m2v2 (since u2 = 0)

Kinetic Energy Conservation:
(1/2)m1u1^2 + (1/2)m2u2^2 = (1/2)m1v1^2 + (1/2)m2v2^2
(1/2)m1u1^2 = (1/2)m1v1^2 + (1/2)m2v2^2 (since u2 = 0)

Simplifying the equations, we get:
m1u1 = m1v1 + m2v2 (equation 1)
m1u1^2 = m1v1^2 + m2v2^2 (equation 2)

Solving for v1:
From equation 1, we can isolate v1:
v1 = (m1u1 - m2v2)/m1

Conclusion:
After the elastic collision, the final velocity of the first particle is given by the equation v1 = (m1u1 - m2v2)/m1. The final velocity of the second particle, v2, can be found by substituting the value of v1 into equation 2.