Answer: Dimensions of A are of length [L]
Dimensions of B are of [tex]LT^{-1}[/tex]
Dimensions of C are of [tex]LT^{-2}[/tex]
Step-by-step explanation:
The given equation is
[tex]x(t)=A+Bt+Ct^{2}[/tex]
Since the dimension on the L.H.S of the equation is [L] , each of the terms on the right hand side should also have dimension of length[L] to be dimensionally valid
Thus
Dimensions of A = [L]
Dimensions of Bt = [L]
[tex]Bt=[L]\\\\[/tex][tex][B][T]=[L][/tex][tex]\\\\\therefore [B]=LT^{-1}[/tex]
Similarly
Dimensions of [tex]Ct^{}2 = [L][/tex]
[tex]Ct^{2}=[L]\\\\[C][T]^{2}=[L]\\\\\therefore [C]=LT^{-2}[/tex]
