Platooning/car following has been considered as a promising approach for improving vehicle efficiency due to the reduction of aerodynamic force when closely following a pilot vehicle. However, safety is a major concern in the close car platooning/following. This paper investigates the minimum inter-vehicle distances required for a passenger vehicle to safely travel behind a heavy-duty truck with three different types of emergency maneuvers. The three emergency maneuvers considered are braking only, steering only, and braking then steering, where steering refers to a single lane change maneuver. Numerical analysis is conducted for deriving the clearance space in the braking only scenario. In addition, simulations are conducted in MATLAB/Simulink, using a bicycle model for the vehicle dynamics, to examine the minimum safe following distance for the other two scenarios. The simulation results show that, for initial vehicle speeds greater than 8 m/s, a lane change maneuver requires the shortest safety distance. Braking followed by lane changing usually requires the largest minimum safety distance.