The velocity of an object varies with time as $V = {A t}^{2} + B t + C$ . Taking the unit of time as $s$ and velocity as ${m s}^{- 1}$ , the units of A, B, C respectively are :

{m s}^{- 3}, {m s}^{- 2}, {m s}^{- 1}

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{m s}^{- 2}, {m s}^{- 1}, {m s}^{- 3}

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{m s}^{- 1}, {m s}^{- 2}, {m s}^{- 3}

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{m s}^{- 1}, {m s}^{- 1}, {m s}^{- 1}

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Solution

The correct option is A ${m s}^{- 3}, {m s}^{- 2}, {m s}^{- 1}$
$V = A t^{2} + B t + C$
All these terms should have some dimension as $V$
$m^{1} s^{- 1} = A s^{2} + B s + C$
$A s^{2} = m^{1} s^{- 1} \Rightarrow A = m^{1} s^{- 3}$
$B s = m^{1} s^{- 1} \Rightarrow B = m^{1} s^{- 2}$
$C = m^{1} s^{- 1} \Rightarrow C = m s^{- 1}$

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