Question

If $x=a+bt+{ct}^2$ , where 'x' is in metre and 't' in second. What are the units of b and 'c'.

Answer 1

Given Data:

The given quantity is $x=a+bt+{ct}^2$

So, unit of $x=\left[a\right]=\left[b\right]\left[t\right]=\left[c\right]\left[{ct}^2\right]$

Here $x$ is in meter and t in seconds so, unit of a,bt and $c{t}^2$ should be equal to unit of x.

Or, [unit of b]*[unit of t] = [unit of x]

units of b $=\frac{unitofx}{unitoft}=\frac{m}{sec}={ms}^{-1}$

Or, [unit of c]*[unit of $t^2$ ] = [unit of x]

units of c $=\frac{unitofx}{unitof{t}^2}=\frac{m}{se{c}^2}=m{s}^{-2}$