This paper analyses the complexity of user behaviour when facing the challenge of using sustainable applications, such as Internet search engines. This paper analyses an acceptance model using extended TAM (Technology Acceptance Model) with Trust as an added external variable. It was suggested that Trust indirectly influences the final Intention to Use with the perceptions of Utility and Ease of Use. To test the proposed model, a survey was carried out with users from different geographical areas of Spain (n=445). The second aim of this study was to understand the complexity of marketing segmentation by separating the application users into different user groups. Users were grouped by their preference of favorite Internet search engine. Unobserved heterogeneity was studied using FIMIX-PLS, and three different user behaviours with search engines were identified. These corresponded to the number of inhabitants who live in the user area. In this way, the impact that the environment has on user choice, acceptance, and use of this type of sustainable applications was shown. The results were checked using PLS-SEM and showed that the model for the adoption of sustainable search engines is explanatory and predictive because confidence and acceptance for this TAM were validated. The conclusions are interesting for developers of environmentally sustainable and responsible applications which want to coincide with current trends to ensure that users prefer them.