if the position of a particle of any instant t is given by x = t^3find

1.	if the position of a particle of any instant t is given by x = t^3find the acceleration of the particle at t = 2 seconds
Answer» $\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$ POSITION equation of particle has been provided. $\dag\:\boxed{\bf{x=t^3}}$ $\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$ We have to find ACCELERATION of particle at t = 2s. $\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$ ✪ Instantaneous VELOCITY : $:\implies\sf\:v=(lim\:\Delta t\to 0)\:\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}$ $:\implies\tt\:v=\dfrac{d(t^3)}{dt}$ $:\implies\bf\:v=3t^2$ ✪ Instantaneous acceleration : $:\implies\sf\:a=(lim\:\Delta t\to 0)\:\dfrac{\Delta v}{\Delta t}=\dfrac{dv}{dt}$ $:\implies\tt\:a=\dfrac{d(3t^2)}{dt}$ $:\implies\bf\:a=6t$ Putting t = 2, we GET $:\implies\tt\:a=6(2)$ $:\implies\boxed{\bf{\red{a=12\:ms^{-2}}}}$