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A question from my textbook is stated below

In an elastic collision

  1. The initial kinetic energy is equal to the final kinetic energy
  2. The final kinetic energy is less than the initial kinetic energy
  3. The kinetic energy remains constant
  4. The kinetic energy first increases then decreases

Given answer is option 1.

I know that there is no loss of energy in elastic collision, so option 1 is correct but as far as I see option 3 which states them same fact as 1 should also be correct.

So is option 3 also correct or something I am missing out?
Please help and thanks for help in advance!!!

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2 Answers 2

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Option 3 is a stronger condition than option 1. It means that the kinetic energy remains constant throughout the collision. For example, this may not be true if there exists a small moment of time where either object is at zero velocity and the object ends up traveling backwards (in the direction it came from).

Physically, this is because the kinetic energy of the object is briefly being converted into elastic potential energy. However, by the end of the collision, all elastic potential energy is converted back into kinetic energy.

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In the moment of collision the kinetic energy $\left(\frac 12mv^2\right)$ is $0,$ because $v = 0$, which means that the option $3$ is not correct.

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