A tractor of mass 5*10^3kg is used to tow a car of mass 2.5*10^3kg.the tractor moves with a speed of 3.0m/s just before the towing rope become taut

Calculate loss in kinetic energy of the system just after the car has started moving

conserve momentum:

5*10^3 * 3 = (5*10^3 + 2.5*10^3)v
Having v, you can now see that
KE before: 1/2 (5*10^3)*3^2
KE after: 1/2 (5*10^3 + 2.5*10^3)v^2
the difference is KE lost