The Question is from neet-physics , and it was created by the author NAGA SAI

Question

What is the dimensional formula of velocity?

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: Option A
## CONCEPT FRAMEWORK
	**Primary Concept**: Dimensional Analysis
	**Related Topics**: Fundamental Quantities, Derived Quantities
	**Prerequisites**: Definition of velocity, Understanding of dimensions
## SOLUTION PATHWAY
**Given Information**:
	Velocity is defined as displacement per unit time.
	Displacement has the dimension of length [L].
	Time has the dimension [T].
**Method & Steps**:
	1. Determine the dimensions of displacement and time.
		Reasoning: Displacement is a length, and time is a fundamental quantity.
		Formula/Rule: Dimensions of displacement = [L], Dimensions of time = [T]
	2. Apply the definition of velocity.
		Working: Velocity = Displacement / Time
		Key Point: Dimensions of velocity = [Dimensions of Displacement] / [Dimensions of Time]
	3.  Combine the dimensions.
		Result: Dimensions of velocity = [L] / [T] = $[LT^{-1}]$
		Verification: The derived dimension matches the standard dimension for velocity.
 ## OPTION ANALYSIS
[A] ✓: The dimensional formula of velocity is length divided by time, which is represented as $[LT^{-1}]$.
[B] :x: This represents acceleration, which is length divided by time squared, $[LT^{-2}]$.
[C] :x: This is not the correct dimensional formula for velocity. It represents a quantity with dimensions of area divided by time.
[D] :x:  This is incorrect. It represents length multiplied by time, which is not the dimension of velocity.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Confusing velocity with speed or acceleration. Speed is the magnitude of velocity, and acceleration is the rate of change of velocity, both have different dimensional formulas.
		2.[Error 2]: Incorrectly using the definitions of other physical quantities. Always start with the fundamental definition of the quantity you are analyzing.
	**Quick Tips**:
		1.[Helpful shortcut]: Remember that velocity is distance/time, so the dimensions will be [Length]/[Time].
		2.[Memory aid]: Use the units of velocity (e.g., m/s) to infer the dimensions [L/T] or $[LT^{-1}]$.

NAGA SAI · Answer

The correct Option is "$[LT^{-1}]$"

NAGA SAI · Answer

$[LT^{-2}]$

NAGA SAI · Answer

$[L^2T^{-1}]$

NAGA SAI · Answer

$[LT]$

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