Question

check the correctness of the relation, Snth= u+a/2(2n-1), where u is initial velocity, a is acceleration and Snth is the distance travelled by the body in nth second.

Answer 1

Given,

A relation Sₙ = u+a/2(2n-1) where u is initial velocity, a is acceleration, and S nth is the distance traveled by the body in nth second.

To Find,

Whether the relation is correct or not.

Solution,

We will use the dimensional analysis to check the correctness of this relation.

The given relation is

Sₙ = u+a/2(2n-1)

The dimensional formula of Sₙ = [LT⁻¹].

Now, solving the R.H.S of the relation

u+a/2(2n-1) = [LT⁻¹]+[LT⁻²][T]

u+a/2(2n-1) = [LT⁻¹]+[LT⁻²⁺¹]

u+a/2(2n-1) = [LT⁻¹]+[LT⁻¹] = [LT⁻¹]

So,

L.H.S = R.H.S

Hence, the given relation is correct.

Answer 2

Given :

$S_{nth} = u+(a/2)(2n-1)$

Verify :

if the equation is correct or not

Explanation:

$S_{nth} = u+(a/2)(2n-1)$

The real formula is ;

$u(1)+(a/2) (1) (2n - 1 )$

where 1 represent    1 sec   as times

LHS = [ L ]

$[ L ] = u(1)=[LT^{-1} ][T]$

                  = [ L ]

$(a/a)(1 )[2n-1] = LT^{-2} [ T ] [ T ]$

                                        = L

[ L ] = [ L ] + [ L ]

hence the formula is correct

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