Step-by-step explanation:
It is given that,
Velocity of particle 1, u₁ = 10 m/s
Velocity of particle 2, u₂ = 5 m/s
Let v₁ and v₂ are the final speed of both particles after the collision. Applying the conservation of momentum as :

......................(1)
For an elastic collision, the coefficient of restitution is equal to 1 as :


................(2)
On solving equation (1) and (2), we get,


So, the speeds of particle 1 and particle 2 after the collision is 5 m/s and 10 m/s respectively. Hence, this is the required solution.