  In this work we formulate the group theoretical description of free fall and
projectile motion. We show that the kinematic equations for constant
acceleration form a one parameter group acting on a phase space. We define the
group elements $\phi_t$ by their action on the points in the phase space. We
also generalize this approach to projectile motion. We evaluate the group
orbits regarding their relations to the physical orbits of particles and
unphysical solutions. We note that the group theoretical formulation does not
apply to more general cases involving a time dependent acceleration. This
method improves our understanding of the constant acceleration problem with its
global approach. It is especially beneficial for students who want to pursue a
career in theoretical physics.
