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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?

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Answer:

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

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