The speed of the combined carts after the collision is 0.25 m/s
Explanation:
We can solve this problem by using the principle of conservation of momentum. In fact, the total momentum of the system must be conserved before and after the collision, so we can write:
[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v[/tex]
where:
[tex]m_1 = 1.0 kg[/tex] is the mass of the first cart
[tex]u_1 = 0.50 m/s[/tex] is the initial velocity of the first cart
[tex]m_2 = 1.0 kg[/tex] is the mass of the second cart
[tex]u_2 = 0[/tex] is the initial velocity of the second cart
[tex]v[/tex] is the final combined velocity of the two carts
Re-arranging the equation and substituting the values, we find: the final velocity:
[tex]v=\frac{m_1 u_1}{m_1+m_2}=\frac{(1.0)(0.50)}{1.0+1.0}=0.25 m/s[/tex]
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