How to remove 'tension from a vehicle'

My issue is that when I weld a vehicle to another vehicle (in my case a flatbed tow truck) it has this ‘tension’ that unless the vehicle is extremely still, when the weld is released it will jump releasing the ‘tension’. I’m not really sure why this is but I presume it’s just a build up of energy it had when it was welded. Is there a way to stop this??