A train car of mass 3,825 kg sits at rest on the track. A second car of mass 5,169 kg moving at 6 m/s slams into it and they stick together. What is the combined speed of the train cars after the collision?

We can solve this problem by using the law of conservation of momentum: in absence of external forces, the total momentum of the two trains must be conserved before and after the collision.

Therefore 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 = 3,825 kg[/tex] is the mass of the first train

[tex]u_1 = 0 m/s[/tex] is the initial velocity of the first train, which is at rest

[tex]m_2 = 5,169 kg[/tex] is the mass of the second train

[tex]u_2 = 6 m/s[/tex] is the initial velocity of the second train

[tex]v[/tex] is the final combined velocity of the two trains after the collision

We can now solve the equation for v, to find the final combined velocity of the two trains:

[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{0+(5169)(6)}{3825+5169}=3.4 m/s[/tex]

So, the final combined speed is 3.4 m/s.

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