Question

If the displacement of a body at an instant is given by:
X=22+At+B root t
Where(x)is measured in meters and (t)is measured in seconds.
Find dimensions of A and B

Answer 1

The given equation is $X=22+At+B {t}^{1/2}$

It is given that |X|=m and |t|=s

where |X| notates the dimensions of the x term which is meters,and |t| notates the dimensions of the t term which is seconds.

For the addition of terms in an equation, each of the terms should posses the same dimensions.

$\because\ |X|=|22|=|At|=|Bt^{1/2}| \\~\\ |X|=|A||t| \newline |A|=m/s\ =ms^{-1}\to(1)\\~\\ |X|=|B||t^{1/2}| \newline |B|=m/s^{1/2} \newline |B|=ms^{-1/2} \to(2)$