Question

x=a+bt+ct^2+d/d-t find dimensions of a,b,c and d​ where x is in metre and t is in second with language ​

Answer 1

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Answer 2

We are given the equation as follows:-

$x=a+b t+c t^{2}+\frac{d}{d-t}$

To find the values of a b and c and d we have to use the dimensional analysis, we are given the unit of X is in metres and T is in seconds so first equating X and a unit of a will be in metres.

Now equating bt = x ⇒ b = x/t = m/s

$\begin{array}{l}{\mathrm{Ct}^{2}=\mathrm{x} \Rightarrow \mathrm{c}=\frac{x}{t^{2}}=\frac{m}{s^{2}}} \\ {\frac{d}{d-t}=\mathrm{x} \Rightarrow \mathrm{x}=\frac{d}{t} \mathrm{d}=\mathrm{xt}=\mathrm{ms}}\end{array}$