Question

Using dimensional symbols prove that the following equation are correct.
A: s=ut+1/2at²

Answer 1

Answer: It is correct

Explanation:

LHS- [L¹]

RHS - [LT^-1 ][T^1] + [LT^-2][T^2]

[L]+ [L] =[L¹]

Answer 2

Answer:

Equation is dimensionally correct.

Explanation:

We need to prove that the following equation is dimensionally correct.

$s=ut+\dfrac{1}{2}at^2$

It is the second equation of kinematics

s is displacement

u is initial speed

t is time

a is acceleration

The dimensional formula of s is [s]=[L]

The dimensional formula of u is [u]=[LT⁻¹]

The dimensional formula of t is [t]=[T]

The dimensional formula of a is [a]=[LT⁻²]

Taking RHS of the above equation,

$ut+\dfrac{1}{2}at^2=[LT^{-1}][T]+\dfrac{1}{2}[LT^{-2}][T^2]\\\\=[L]+{L}\\\\=[L]$

The dimensional formula of the LHS of the equation is $[L]$. It means that the given equation is dimensionally correct.

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Dimensional analysis

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