Negative energy is impossible. If the cars have -100,000 J after the crash, the total difference is 300,000 Joules. Furthermore, the equation for kinetic energy is

\(\displaystyle KE = \frac{1}{2} m v^2\)

So the only way to get negative kinetic energy is to have negative mass, which is not the case for cars.

I think if you read my post carefully it's OK ....

If the frame of reference is on one car we could be forgiven for thinking the energy at impact is 200,000 ,

**but it can't be** , and this is explained because the frame of reference is moving which gives an apparent KE of the crashed stationary cars of 100,000 in the other direction ...we have to subtract it from the 200,000

Hopefully other members will give their thoughts.

Let's look at things in another way .... our frame of reference is on one car , the other impacts at 20m/sec , but they will not come to rest

**in our frame of reference** the whole crashed mass is travelling at 10m/sec

energy in colliding car at 20m/sec = 200,000

energy in moving mass of crashed two cars = 100,000

these two have to be subtracted to get the correct figure of 100,000

It's a mathematical convenience and is valid to have one figure negative .