We can use this expression to calculate the velocity of a
cart launched by a spring on the air-track. From the work kinetic
energy theorem we have
Where we have assumed that the initial kinetic energy 
and that the brick leaves the spring for 
and we
denote the initial compression of the spring by 
, which will
be a negative number here indicating compression to the negative side of the
origin for the x-axis. Solving for 
we get
Note that we cannot predict the direction of the velocity (its sign in one
dimension) because our expressions start off containing squared velocities.
We measure the spring constant by hanging a mass, M from the spring. In equilibrium
Choosing M=0.5 kg we measure 
m so that for our spring
We launch the cart with mass m=0.397 kg
through a compression of the spring to
m. Thus we predict
We do the experiment which shows that
which is perfectly consistent with this result.
Note also how the cart bounces back and forth after the experiment.
This indicates that the forces which dominate this experiment conserve
mechanical energy. We say that they are conservative forces.