Two identical objects are moving directly toward one another at the same speed v. ~v −~v m m what is the total kinetic energy of the system of the two objects?

Since energy is a scalar, the total kinetic energy of the system of the two objects is mv².

Let "m" represent the mass of the two identical objects and "v" represent their speed or velocity.

Total kinetic energy of a system is the same as the addition or sum of the kinetic energies resulting from the different or each type of motions.

Hence,

the total kinetic energy of the two object is:

Therefore, since energy is a scalar, the total kinetic energy of the system of the two objects is mv².

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Explanation:

Calling m the mass of each object and v its speed, the kinetic energy of one object is given by

As we can see, the value of the kinetic energy depends only on the speed, not on the direction of the velocity. Therefore, the kinetic energy of the second object is the same:

And so, the total kinetic energy is