The conservation of the total momentum demands that the total momentum before the collision is the same as the total momentum after the collision , and is expressed by the equation Likewise , the conservation of the total kinetic energy is expressed by the equation These equations may be solved directly to find vi when ui are known or vice versa .
The formula for kinetic energy is : So , using the same variables as before : The initial kinetic energy is : The final kinetic energy is : Setting the two to be equal ( since the total kinetic energy remains the same ) : These equations may be solved directly to find vi when ui are known or vice versa .