Question

derive snth=v0+a/2(2n-1)
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Answer 1

Answer:

Here, S=u+(1/2)*a*(2n-1) this equation is used to find displacement of body in nth second.

LHS

So, S(nth) = displacement of body in nth second

i.e S(nth) = [L]/[T] = [LT^-1] dimensionally

RHS

Now, U+(1/2)*a*(2n-1) = where,

U= initial velocity = [LT^-1]

a= acceleration = [LT^-2]

2n-1= n=time = [T]

1/2=dimensionless = [M°L°T°]

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U+(1/2)*a*(2n-1)= [LT^-1]+[LT^-2]*[T]

[LT^-1]+[LT-^1]=[LT^-1] by principle of homogeneity.

As LHS= RHS dimensionally i.e [LT^-1]

Therefore, it is dimensionally correct.