# Calculate Velocity of Cars in Elastic Collision

## Explanation:

**Given:**

- Cart 1 speed is twice that of Cart 2
- Cart 2 inertia is twice that of Cart 1
- Initial speed of Cart 2 is v

To calculate the velocity of cart 1 after an elastic collision on a low-friction track, we need to apply the principles of momentum and kinetic energy conservation.

**Equations for Elastic Collision:**

Velocity of cart 1 after collision (v1) = [(m1 - m2) / (m1 + m2)] * u1 + [(2m2) / (m1 + m2)] * u2

Velocity of cart 2 after collision (v2) = [(2m1) / (m1 + m2)] * u1 - [(m1 - m2) / (m1 + m2)] * u2

**Given:**

m1 = m, m2 = 2m (mass of cart 1 and cart 2 respectively)

u1 = 2u, u2 = u (initial velocities of cart 1 and cart 2 respectively)

**Solving for v1:**

v1 = [(m - 2m) / (3m)] * 2u + 2 * [(2m) / (3m)] * u

v1 = (2u / 3)

**Solving for v2:**

v2 = [(2m) / (3m)] * (2u) - [(m - 2m) / (3m)] * u

v2 = (5u / 3)

Therefore, the speed of cart 1 right after the collision in an elastic collision scenario is 2u/3.

**Final Answer:**

To find the velocity of cart 1 after an elastic collision on a low-friction track, we use the principles of momentum and kinetic energy conservation to create two equations and solve them to determine the final velocities of both carts.