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

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Solution

Given Data:

The given quantity is $x = a + b t + {c t}^{2}$
So, unit of $x = [a] = [b] [t] = [c] [{c t}^{2}]$
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 $= \frac{u n i t o f x}{u n i t o f t} = \frac{m}{s e c} = {m s}^{- 1}$
Or, [unit of c][unit of $t^{2}$ ] = [unit of x]
units of c $= \frac{u n i t o f x}{u n i t o f t^{2}} = \frac{m}{s e c^{2}} = m s^{- 2}$

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