Answer:
The rest energy of the particle is

The velocity of the particle is

Step-by-step explanation:
From the question we are told that
The rest energy of the original particle is

The speed of the particle is

The rest energy the first particle is

The rest energy of the second particle is

The first particle has a kinetic energy of
positive x
The second particle has a kinetic energy of
negative x
The total energy of the first particle is

Substituting values


The total energy of the first particle is



The momentum of the first particle can be mathematically evaluated using this expression



The final energy of both particle is mathematically evaluated as


The momentum of the first particle can be mathematically evaluated using this expression

The negative sign shows that he direction is negative x-axis


The final momentum of both particle is mathematically evaluated as

Substituting value

According to the law of conservation of momentum and the conservation of energy the final energy and momentum of both particle must be equal to the initial energy of the original particle
Then the rest energy is mathematically represented as

Substituting values


The velocity of the original particle can be obtained from the mathematical expression as follows
![v = c\sqrt{1 - [((mc^2))/(E)]^2 }](https://img.qammunity.org/2021/formulas/physics/college/o5ts4j577x9k1crgpvv78fx7f5ojr2io9v.png)
Where c is the speed of light with value

Substituting value
