# numerical problem

Given that displacement y of a particle moving along a straight line at time t is given by the equation

x = a1 + a2t + a3t^2 where a1, a2, and a3 are constants

We know that velocity is rate of change of displacement

v = dx/dt = d/dt (a1 + a2t + a3t^2)

dx/dt = a2 + a3 x 2 x t

dx/dt = a2 + 2a3t

We also know that acceleration is rate of change of velocity

a = dv/dt = d/dt(a2 + 2a3t)

a = dv/dt = 2a3

Hence, the acceleration of the particle will be 2a3.