Answer: [tex]3\ m/s,\ 20,00\ J[/tex]
Explanation:
Given
Mass of the first car [tex]m_1=5000\ kg[/tex]
Mass of the second car [tex]m_2=5000\ kg[/tex]
The velocity of the first car is [tex]v_1=5\ m/s[/tex]
The velocity of the second car is [tex]v_2=1\ m/s[/tex]
Conserving momentum, take [tex]v_o[/tex] as the velocity after coupling
[tex]\Rightarrow m_1v_1+m_2v_2=\left( m_1+m_2\right)v_o\\\Rightarrow 5000\times 5+5000\times 1=\left( 10,000\right)v_o\\\\\Rightarrow v_o=\dfrac{25,000+5000}{10,000}\\\\\Rightarrow v_o=\dfrac{30,000}{10,000}\\\Rightarrow v_o=3\ m/s[/tex]
[tex]\text{Initial kinetic Energy }K_1=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2\\\\\Rightarrow K_1=\frac{1}{2}\times 5000\left( 5^2+1^2\right)\\\\\Rightarrow K_1=65,000\ J\\\\\\\text{Final Kinetic Energy}\ K_2=\frac{1}{2}\left(m_1+m_2\right)v_o^2\\\\\Rightarrow K_2=\frac{1}{2}\times 10,000\times 3^2\\\\\Rightarrow K_2=45,000\ J\\\\\text{Kinetic energy lost is equivalent to change in Initial and final energy i.e.}\\\\\Rightarrow K_1-K_2=65,000-45,000\\\\\Rightarrow K_1-K_2=20,000\ J[/tex]
