To solve the dynamical system as a motion of a particle with the help of differential equation and some integral transformation. The Elzaki transformation and Laplace transformation methods are used to solve the equation of motion of a particle. Since last few decades the problem on motion of particle had been solved by many mathematical methods. In this paper motion of the problem solved with Elzaki transform and compared the results with Laplace transform. Whenever applied and compared the Laplace and Ezaki methods to motion of particle problem it was confirmed that both methods gave similar results.