Newtons laws of motion. Every action has an equal and opposite reaction. pulling UP on the handlebars pushes you DOWN on the pedals with the same force.
Before the collision, the two balls' total momentum is
(1 kg) (+1 m/s) + (1 kg) (-1 m/s) = 0
After the collision, the combined balls have velocity v such that
(1 kg + 1 kg) v = 0
since momentum is conserved. Equivalently,
(2 kg) v = 0
It follows that v = 0, meaning after impact the balls are stuck together and motionless.
