The velocity v of a particle is given in terms of time t by the equation v=at +bt+c The dimensions of a,b,c are respectively

v=at=bt+c and t=c⇒ c=T.⇒ t+c=T⇒ bT=LT−1⇒ b=L and a=LT−2So, a=LT−2,b=L,c=T

The velocity v of a particle is given in terms of time t by the equation v=at +bt+c The dimensions of a,b,c are respectively

v=at=bt+c and t=c⇒ c=T.⇒ t+c=T⇒ bT=LT−1⇒ b=L and a=LT−2So, a=LT−2,b=L,c=T

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The velocity $v$ of a particle is given in terms of time $t$ by the equation $v = a t + \frac{b}{t + c}$ The dimensions of $a, b, c$ are respectively

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$L^{2}, T, L T^{2}$

$L T^{- 2}, L, T$

$L, L T, T^{2}$

$L T^{2}, L T, L$

answer is C.

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$[v] = [a t] = [\frac{b}{t + c}]$ and $[t] = [c]$

$\Rightarrow [c] = T$

. $\Rightarrow [t + c] = T$

$\Rightarrow \frac{[b]}{T} = L T^{- 1}$

$\Rightarrow [b] = L$ and $[a] = L T^{- 2}$

So, $[a] = L T^{- 2}, [b] = L, [c] = T$

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The velocity v of a particle is given in terms of time t by the equation v=at +bt+c The dimensions of a,b,c are respectively

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The velocity $v$ of a particle is given in terms of time $t$ by the equation $v = a t + \frac{b}{t + c}$ The dimensions of $a, b, c$ are respectively