Development of earthquake early warning system (EEWS) is in advanced stage in different parts of the world including India. The success of EEWS for mitigating seismic risk and saving human lives has been well documented in Mexico, Japan, and Taiwan, where the alert is issued to the public. Taking advantage of the recorded ground motion data from the network of Institute of Seismological Research (ISR), India, with magnitude range 3.0–5.2, we investigated correlations between various ground motion parameters like peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), P_a, P_v, P_d, and τ_c.Three- to 5-s time windows are considered to measure P_a, P_v, P_d, and τ_c from the vertical component of the waveforms. Linear regression analysis is performed at various time steps (3- to 5-s time interval). The results show that considering 4- and 5-s windows exhibits good relationships compared with the 3-s window, which shows more scattering. These empirical relationships using τ_c and M as well as P_d and M are very helpful in determining the earthquake magnitude and subsequently taking steps toward risk assessment.