We introduce a novel approach to user authentication called Motion ID. The method employs motion sensing provided by inertial measurement units (IMUs), using it to verify the persons identity via short time series of IMU data captured by the mobile device. The paper presents two labeled datasets with unlock events: the first features IMU measurements, provided by six users who continuously collected data on six different smartphones for a period of 12 weeks. The second one contains 50 hours of IMU data for one specific motion pattern, provided by 101 users. Moreover, we present a two-stage user authentication process that employs motion pattern identification and user verification and is based on data preprocessing and machine learning. The Results section details the assessment of the method proposed, comparing it with existing biometric authentication methods and the Android biometric standard. The method has demonstrated high accuracy, indicating that it could be successfully used in combination with existing methods. Furthermore, the method exhibits significant promise as a standalone solution. We provide the datasets to the scholarly community and share our project code.