This paper analyzes the multi-hop connectivity properties of linear vehicular ad hoc networks (VANETs) based on a physical layer based quality of service (QoS) criterion in terms of average end-to-end path outage probability. Under this approach, a multi-hop path joining a pair of vehicles is considered to be connected if and only if the average end-to-end path outage probability meets a target requirement. An analytical model to find the average end-to-end path outage probability of a connected path is presented. We then investigate the minimum transmit power required to ensure that the network is connected satisfying an average path outage probability constraint. We also determine the maximum number of hops, a packet from the source can traverse while satisfying the desired average path outage probability criterion. The validity of the theoretical analysis is verified by extensive simulation studies.