Answer:
[tex]2.09\ \text{m/s}[/tex]
[tex]22298.4\ \text{J}[/tex]
Explanation:
m = Mass of each the cars = [tex]1.6\times 10^4\ \text{kg}[/tex]
[tex]u_1[/tex] = Initial velocity of first car = 3.46 m/s
[tex]u_2[/tex] = Initial velocity of the other two cars = 1.4 m/s
v = Velocity of combined mass
As the momentum is conserved in the system we have
[tex]mu_1+2mu_2=3mv\\\Rightarrow v=\dfrac{u_1+2u_2}{3}\\\Rightarrow v=\dfrac{3.46+2\times 1.4}{3}\\\Rightarrow v=2.09\ \text{m/s}[/tex]
Speed of the three coupled cars after the collision is [tex]2.09\ \text{m/s}[/tex].
As energy in the system is conserved we have
[tex]K=\dfrac{1}{2}mu_1^2+\dfrac{1}{2}2mu_2^2-\dfrac{1}{2}3mv^2\\\Rightarrow K=\dfrac{1}{2}\times 1.6\times 10^4\times 3.46^2+\dfrac{1}{2}\times 2\times 1.6\times 10^4\times 1.4^2-\dfrac{1}{2}\times 3\times 1.6\times 10^4\times 2.09^2\\\Rightarrow K=22298.4\ \text{J}[/tex]
The kinetic energy lost during the collision is [tex]22298.4\ \text{J}[/tex].
