The distance x covered by a paritcle in one dimensional motion varies with time t as x^2= at^2+2 bt + c. If the acceleration of the particle depends…

The distance $\displaystyle x$ covered by a paritcle in one dimensional motion varies with time $\displaystyle t$ as $\displaystyle x^2=\mathrm{at}^2+2 \mathrm{bt}+\mathrm{c}$. If the acceleration of the particle depends on $\displaystyle x$ as $\displaystyle x^{-\mathrm{n}}$, where n is an integer, the value of n is \_\_\_\_.