Question

Write the dimensional formula of velocity.

Answer 1

In order to find the dimensional formula of velocity, we need to know the formula of velocity i.e., velocity, $v = \dfrac{s}{t}$ where $s =$displacement, $t =$time taken.
Then we need to find units of velocity, displacement and time in the terms of fundamental quantities.

Complete step-by-step solution:
Fundamental quantities: The quantities which are independent of any other quantities are called fundamental quantities.
Dimensional formula: The expression showing the relationship between the fundamental quantities and expressing the powers of fundamental quantities to be raised to obtain one unit of derived quantity is called dimensional formula.
E.g., let $K$be a quantity then it’s dimensional formula=${[M]^a}{[L]^b}{[T]^c}$where $M =$mass, $L =$Length and $T =$time
Now, Velocity, $v = \dfrac{s}{t} - - (i)$
SI unit of displacement, $s = m$(meter), $$t =$$$s$(Second) Substituting the above value in equation$(i)$we get:$ v = \dfrac{m}{s} \\
v = m{s^{ - 1}} \\ $Thus, SI unit of velocity is$m{s^{^{ - 1}}}$In dimensional formula we represent metre as$M$, second as$S$So, Dimensional Formula of velocity=$\left[ M \right]{\left[ T \right]^{ - 1}}$Final answer: The dimensional formula of velocity is$\left[ M \right]{\left[ T \right]^{ - 1}}$

Note: There are $7$fundamental quantities that don’t depends on other quantities are as follows:
Mass (Kilogram)
Time (seconds)
Length (metre)
Temperature (kelvin)
Luminous intensity (candela)
Amount of substance (mole)
Electric current (ampere)