A particle moves along the x-axis so that at any time t≥0 its velocity is given by v (t) = t^2In (t+2). What is the acceleration of the particle at time t=6

Acceleration is the change of velocity per unit change of time. In this case, given the velocity equation, we can get the acceleration of the particle by taking the first derivative of the equation. v' (t) = t^2 (1/t+2) + 2t In (t+2). substituting t = 6, acceleration is equal to 29.45 m/s2.