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  4. Position of a body with acceleration a is given by x=k am tn, here t is time, find the dimension of m and n

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Q. Position of a body with acceleration $a$ is given by $x=k a^{m}\, t^{n}$, here $t$ is time, find the dimension of $m$ and $n$

ManipalManipal 2013Physical World, Units and Measurements

Solution:

Position $x=K a^{m} \,t^{n}$
Writing the dimension on the both sides.
$\left[M^{0}\, L \,T^{0}\right]=\left[L \,T^{-2}\right]^{m}[T]^{n}$
$\left[M^{0} \,L^{m} \,T^{-2 m+n}\right]$
On comparing both sides.
$m=1$
$-2 m+n=0$
$n=2 m=2 \times 1=2$