Question

Write down the units and dimensional formulae of following physical quantities:
Speed

Answer 1

Units and dimensional formula of speed:

• Speed can be described as the distance covered per unit time by an object.
• Mathematically, it can be given as $Speed=\frac{Dis\tan ce}{Time}$ .
• So, the unit of speed $=\frac{Dis\tan ce}{TIme}=\frac{m}{s}=m{s}^{-1}$, i.e., metres per second.
• Dimensional formula of speed:
  $$\begin{gathered} Speed=\frac{Dis\tan ce}{Time} \\ \hspace{0.17em}=\left(length\right)\times {\left(time\right)}^{-1} \\ \Rightarrow \left[Speed\right]=\left[L\right]\left[T^{-1}\right] \\ =\left[L{T}^{-1}\right] \end{gathered}$$

Thus, the unit of speed is $m{s}^{-1}$ and its dimensional formula is $\left[L{T}^{-1}\right]$.