Question

The position, x, of an object is given by the equation x = A + Bt +Ct2, where t refers to time. What are the dimensions of A, B, and C?

Answer 1

Answer: Dimensions of A are of length [L]

Dimensions of B are of $LT^{-1}$

Dimensions of C are of $LT^{-2}$

Step-by-step explanation:

The given equation is

$x(t)=A+Bt+Ct^{2}$

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]

$Bt=[L]$$[B][T]=[L]$$\\\\\therefore [B]=LT^{-1}$

Similarly

Dimensions of $Ct^{}2 = [L]$

$Ct^{2}=[L]\\\\[C][T]^{2}=[L]\\\\\therefore [C]=LT^{-2}$