This research represents exploratory work into an area that offers interesting perspectives with regard to the issues of trust and acceptance in driverless vehicles. It tries to answer questions related to how trust, and therefore acceptance, is affected by the different elements (visible and not visible) of an autonomous car. In order to accomplish this, an extensive literature review was conducted, based on which a survey was developed and later on deployed. The survey was addressed to those that have never been in contact so far with a driverless car, trying to grasp the a priori perceptions of trust in this new technology. A total number of 429 participants started the survey from which 111 respondents partially completed it and a further 291 fully completed the online questionnaire. The respondents were firstly asked to state what are the most important aspects that would influence their trust into a driverless car. Following this initial question, they were asked to grade on a seven points Likert scale their agreement with a series of statements that were trying to reveal how their trust would be affected by the different aspects of a driverless car. One of the most important findings of this research is related to the issue of anthropomorphism ( the ability of the car to act human), as most of the participants considered it has very little importance on their levels of trust, furthermore it being graded last on a scale of the most important factors that influence their trust levels. This finding draws attention to an important issue: the ethical design of a vehicle, adding a new dimension to the existent research on the theme of anthropomorphism as an increasing factor of trust levels and acceptance. Other interesting trends that can be deducted from this research look into the possible connections that exist between privacy and sharing information (V2X) and the way the users perceive that this might affect their trust into the system. The necessity for the existence of a balance between the information that is shared and made available to the car and the privacy limits that have to be put in place, although not totally clear to the respondents, is one of grave importance as individuals seem to be more willing to give up their right to privacy in situations where their personal safety is at stake. One of the points agreed upon by researchers is that in order to build a trust relationship between two entities (human and autonomous vehicle, in this case) there must be an assurance that one of them will act in a predictable manner. In order to explore this area, the participants were asked to grade the way in which they believe the decision making process of the vehicle and its ability to drive in a similar manner as a human driver would influence their trust and acceptance of the vehicle. The findings of this exploratory survey offer a new direction of research into this area, one which has at its core the need to develop these technologies around the needs of the users, with a focus on the trustworthiness of the vehicle.