Question

The position of particle at any time '$t$' is given by $S\left(t\right)=\frac{V_0}{a}[1-e^{-at}]$ where $a>0$ and $V_0$ is constant velocity. The dimensions of $a$ are:

• A. $T^1$
• B. $T^{-1}$
• C. $L^1{T}^{-1}$
• D. $L^{-1}T$

Answer 1

Answer: (B)

$T^{-1}$

$s\left(t\right)=\frac{V_0}{a}(1-e^{at})$
$\Rightarrow s\left(t\right)$ has the dimension of $M^0{L}^1{T}^0$
$\frac{V_0}{a}$ should also have the dimension of $M^0{L}^1{T}^0$
$\Rightarrow M^0{L}^1{T}^0=\frac{L^1{T}^{-1}}{a}$
$\Rightarrow a=T^{-1}$