Research has shown that trust is an essential aspect of human-computer interaction directly determining the degree to which the person is willing to use the system. An automatic prediction of the level of trust that a user has on a certain system could be used to attempt to correct potential distrust by having the system take relevant actions like, for example, explaining its actions more thoroughly. In this work, we explore the feasibility of automatically detecting the level of trust that a user has on a virtual assistant (VA) based on their speech. We use a dataset collected for this purpose, containing human-computer speech interactions where subjects were asked to answer various factual questions with the help of a virtual assistant, which they were led to believe was either very reliable or unreliable. We find that the subject's speech can be used to detect which type of VA they were using, which could be considered a proxy for the user's trust toward the VA's abilities, with an accuracy up to 76\%, compared to a random baseline of 50\%. These results are obtained using features that have been previously found useful for detecting speech directed to infants and non-native speakers.