Write down the units and dimensional formulae of following physical quantities:
$A c c e l e r a t i o n = \frac{v e l o c i t y}{t i m e}$

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Solution

Units and dimensional formula of acceleration:
Acceleration can be described as the rate of change of velocity of an object with respect to time.
Mathematically, it can be given as $A c c e l e r a t i o n = \frac{v e l o c i t y}{t i m e}$ .
So, the unit of acceleration $= \frac{m s^{- 1}}{s} = m s^{- 2}$ , i.e., meters per second square.
Write the formula of acceleration in terms of fundamental quantities to find the dimensional formula:
$A c c e l e r a t i o n = \frac{(d i s \tan c e / t i m e)}{t i m e} = \frac{d i s \tan c e}{{(t i m e)}^{2}} = \frac{l e n g t h}{{(t i m e)}^{2}} = l e n g t h \times {(t i m e)}^{- 2}$
$[A c c e l e r a t i o n] = [L] \times [T^{- 2}] = [L T^{- 2}]$
Thus, the unit of acceleration is $m s^{- 2}$ and its dimensional formula is $[L T^{- 2}]$ .

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