# Elastic Collision In One Dimension

In elastic collision involves two bodies moving initially along the same straight line, striking against each other without loss of kinetic energy and continuing to move along the same state line after collision.

Let to bodies A and B of masses m and m moving along the same straight line with velocities u₁ and u₂ respectively and let u₁>u₂.

After collision bodies A and B moving with velocities v₁ and v₂ in the same direction such that v₂>v₁.

As linear momentum is conserved in any collision, then we get

Hence, In one dimensional elastic collision, relative velocity of separation after collision is equal to relative velocity of approach before collision.

#### Velocities Of Bodies After The Collision

From equation (IV)

u₁ – u₂ = v₂ – v₁

v₂ = v₁ + u₁ – u₂

Now, putting the value of v₂ in equation (i)

##### Velocity Of Body A After Collision

Similarly by putting the value of v₁ from equation (IV) in equation (I), we get

#### Special Cases:

###### Case-I:- When two bodies of equal masses collide.

Hence, When two bodies of equal masses undergo perfectly elastic collision in One dimension, their velocities are just interchanged.

###### Case-II:- When light body collides against a massive stationery body.

Hence, When a light body collides against a massi body at rest, the light body rebounds after the collision with an equal and opposite velocity while the massive body practically remains at rest.