This paper investigates the problem of determining the speed and the attitude of a vehicle equipped with a monocular camera and inertial sensors. The vehicle moves in a 3D unknown environment. It is shown that, by collecting the visual and inertial measurements during a very short time interval, it is possible to determine the following physical quantities: the vehicle speed and attitude, the absolute distance of the point features observed by the camera during the considered time interval and the bias affecting the inertial measurements. In particular, this determination, is based on a closed form solution which analytically expresses the previous physical quantities in terms of the sensor measurements. This closed form determination allows performing the overall estimation in a very short time interval and without the need of any initialization or prior knowledge. This is a key advantage since allows eliminating the drift on the absolute scale and on the vehicle orientation. In addition, the paper provides the minimum number of distinct camera images which are needed to perform this determination. Specifically, if the magnitude of the gravity is unknown, at least four camera images are necessary while if it is a priori known, three camera images are necessary. The performance of the proposed approach is evaluated by using real data.