According to Newtons second law of motion, the rate of change of momentum is equal to the force. if the mass of an object is constant the force can be given as a product of mass and acceleration.
Mathematically,
\[force= mass*acceleration\]
\[[Force]= [mass]*[\frac{velocity}{time}]\]
\[[Force]= [mass]*[\frac{\frac{length}{time}}{time}]\]
\[[Force]= [mass]*[length]*[time]^{-2}\]
Therefore, the dimensions of the force is
\[[F]=[M^{1},L^{1},T^{-2}]\]
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