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Physics of a Rear-End Collision

Two cars travel in the same direction on a slippery road. Initially they are 16 m apart. They have a rear-end collision at time and travel together after that. Their masses are (blue) and (red), and their velocities are and . Using conservation of momentum, the velocity after the collision is calculated, as is the kinetic energy lost in the collision.

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The velocity of the cars after collision is . The kinetic energy lost is , where and are the kinetic energies of each car before the collision, and is the kinetic energy of both cars considered as a single body after the collision.
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