On a frictionless track, cart 1 is moving with a constant, rightward (+) velocity of 1.0m/s. Cart 2 is also moving rightward with constant velocity of 5.0m/s. After a while, cart 2 collides cart 1 from behind. (It is an elactic collision.) If the final velocity of cart 2 becomes 3.0m/s, what is the final velocity of cart 1?

The final velocity of cart 1 is 3m/s

Explanation:

From principle of conservation of linear momentum, which states that sum of the momentum before collision is equal to the sum of the momentum after collision.

Momentum, P is given as mass x velocity.

ΔP = Δmv = m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Assumptions:

If the two carts are moving on frictionless track, then limiting frictional forces due to their weights are negligible. After the elastic collision, the two carts will move separately with different velocity

u₁ + u₂ = v₁ + v₂;

where;

u₁ and u₂ are the initial velocity for cart 1 and cart 2 respectively

v₁ and v₂ are the final velocity for cart 1 and cart 2 respectively

1 m/s + 5 m/s = v₁ + 3m/s

6 m/s = v₁ + 3m/s

v₁ = 6 m/s - 3m/s = 3m/s

Therefore, the final velocity of cart 1 is 3m/s