Interactions between the computing units and the physical environment in Cyber-Physical Systems (CPSes) are considered to verify safety properties, i.e. ensuring the un-intentional side-effects of cyber-physical interactions are within desired limits. A Linear 1 space dimension Spatio-Temporal Hybrid Automata (LlSTHA) is defined to capture the effects of the interactions, in both time and space. Aggregate effects of interactions due to concurrent operations in the computing entities are expressed as a set of interdependent partial differential equations associated with dedicated modes of the LlSTHA model. A time and space bound LlSTHA reachability analysis algorithm is proposed for safety verification, which provides reachable states of the L1STHA with an arbitrary accuracy . The runtime of the algorithm depends on the requested accuracy. The usage of the LlSTHA modeling and analysis is demonstrated for medical CPSes such as infusion pumps.