If two objects are moving in opposite directions, I know that you choose one direction to be negative and one to be positive, and then find the sum of momentum. What I'm not sure about is kinetic energy. To find the total kinetic energy of the objects moving in opposite directions, would one of the values for kinetic energy be positive and the other negative, or would they both be positive?

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Originally Posted by HepZeba

.... To find the total kinetic energy of the objects moving in opposite directions, would one of the values for kinetic energy be positive and the other negative, or would they both be positive?

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Kinetic energy is a scalar quantity, not a vector - which means it has magnitude but no direction, so there is no such thing as a "negative" kinetic energy. For moving objects you typically use KE = 1/2 mv^2; note that the quantity v squared is always a positive number (or maybe 0), even if v itself is a negative number.