Let the speeds of drivers e and n prior to the collision be denoted by ve and vn, respectively. find v2, the square of the speed of the two-car system the instant after the collision.
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Make a momentum balance: m_e · v_e + m_n · v_n = (m_e + m_n) · v where v is the speed of the two cars instant after the collision. Because the cars have the same mass, this simplifies to v_e + v_n = 2v The square of the speed instant after collision is: v² = 1/4·(v_e + v_n)²