Question

The dimensional formula of acceleration is ______.

Answer 1

Prerequisite: Units of derived quantities

1. A dimensional formula is the formula of a physical quantity in terms of the powers of fundamental quantities.
2. The formula of acceleration is: $Acceleration=\frac{Velocity}{Time}$
3. Write the formula of acceleration in terms of fundamental quantities to find the dimensional formula:
   $$\begin{gathered} Acceleration=\frac{(dis\tan ce/time)}{time} \\ =\frac{dis\tan ce}{{\left(time\right)}^2} \\ =\frac{length}{{\left(time\right)}^2} \\ =length\times {\left(time\right)}^{-2} \end{gathered}$$
   $\left[Acceleration\right]=\left[L\right]\times \left[T^{-2}\right]=\left[L{T}^{-2}\right]$
   

Thus, the dimensional formula of acceleration is $\left[L{T}^{-2}\right]$.