I have a question about kinetic energy:
Imagine two vehicles with velocities $v_1$ going at $30 \frac{\text{m}}{\text{s}}$ and $v_2$ at $50\frac{\text{m}}{\text{s}}$.
If they hit each other, will the kinetic energy be
$$ \frac{1}{2}m(v_1+v_2)^2 \text{ or } \frac{1}{2}m(v_1^2 +v_2^2) \text{ ?}$$
It should be the second formula, otherwise there would be more energy than necessary to reach this speed, but I don't understand why it is this way.
After all, if you had a vehicle hitting a wall at $80\frac{\text{m}}{\text{s}}$ it would have the same energy as 2 vehicles hitting each other at $50\frac{m}{s}$ and $30\frac{m}{s} $, right?
Can somebody explain this apparent discrepancy to me?