Middle School

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

Answer :

The final combined speed of the two trains is 3.4 m/s

Explanation:

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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