The detection of Generalized Tonic Clonic Seizures (GTCS) and Falls is of utmost importance due to the increase in prevalence of epilepsy and Sudden Death in Epileptic Patients during CoVID-19 pandemic, and prevention of serious injuries in Fall risk groups such as elderly requiring continuous monitoring for disease management and assisted living etc. Monitoring of Activities of Daily Living (ADLs) can assist in the detection of symptoms and onset of neurological disorders such as Alzheimer's, stroke, and epileptic seizures. With a host of embedded sensors, improved memory, enhanced processing capabilities and availability to masses, smartphones can be used for Human Activity Recognition (HAR) through continuous monitoring of ADLs. This paper presents a tri-axial accelerometer-based approach to detect and classify activities performed by individuals by applying machine learning algorithms including RF, J48, NB, LMT and SVM to movement data. Movement data is collected in real-time from the embedded accelerometer of a smartphone worn by individual on upper-left arm in unconstraint environment. It is pre-processed using time and frequency domain analysis and spatial domain features are computed. Supervised machine learning techniques are applied to classify ADLs into five classes based on the intensity of movements: Stationary, Light Ambulatory, Intense Ambulatory, GTCS and Falls. We also used training data from MyNeuroHealth dataset collected from 23 individuals including epilepsy patients. Based on gathered results, Random Forest outperforms other classifiers with classification accuracy of 99.6% for stationary, 81.5% for light ambulatory, 99.8% for intense ambulatory and GTCS, and 97.2% for Falls corresponding to training data of 14000 samples. To date, activity classification in our system has been implemented on cloud instead of mobile phone application as subjects are using smartphones with dissimilar software and hardware specifications for assisted living applications.