Let the dimensional formula of energy in terms of force ($F$), acceleration ($A$), and time ($T$) be: $[E] = [F]^a [A]^b [T]^c$ Writing the dimensions of each physical quantity in terms of fundamental quantities $M, L, T$: $[ML^2T^{-2}] = [MLT^{-2}]^a [LT^{-2}]^b [T]^c$ $[ML^2T^{-2}] = [M^a L^{a+b} T^{-2a-2b+c}]$ Equating the powers of $M, L,$ and $T$ on both sides, we get: For $M$: $a = 1$ For $L$: $a + b = 2 \implies 1 + b = 2 \implies b = 1$ For $T$: $-2a - 2b + c = -2 \implies -2(1) - 2(1) + c = -2 \implies -4 + c = -2 \implies c = 2$ Substituting the values of $a, b,$ and $c$, we get the dimensions of energy as $[FAT^2]$.