One particle has mass m and a second particle has mass 2m. The second particle is moving with speed v and the first with speed 2v. How do their kinetic energies compare?

Explanation:

The formula for kinetic energy to be used here is 1/2mv².

If the first particle is "particle a" and the second particle is "particle n"; there kinetic energies (K.E) will be

K.Eₐ = 1/2.m2v² = mv²

K.Eₙ = 1/2.2mv² = mv²

From the above, it can be said that there kinetic energies are the same.

NOTE that the m and v used in the question means mass and velocity respectively.

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