Dynamics of shallow impact cratering
  We present data for the time-dependence of wooden spheres penetrating into a loose non-cohesive packing of glass beads. The stopping time is a factor of three longer than the time $d/v_\circ$ needed to travel the total penetration distance $d$ at the impact speed $v_\circ$. The acceleration decreases monotonically throughout the impact. These kinematics are modelled by a position- and velocity-dependent stopping force that is constrained to reproduce prior observations for the scaling of the penetration depth with the total drop distance. 
M.A. Ambroso, R.D. Kamien, and D.J. Durian