A body travels uniformly a distance of (S + ∆S) in a time (t±Δt). What may be the condition so that body within the error limits move with a velocity St±ΔSΔt;

Δt t + S ( Δt ) 2 ( ΔS ) t 2 = ± 1

A body travels uniformly a distance of (S + ∆S) in a time (t±Δt). What may be the condition so that body within the error limits move with a velocity St±ΔSΔt;

Δt t + S ( Δt ) 2 ( ΔS ) t 2 = ± 1

Δt t + ( ΔS ) t S ( Δt ) = ± 1

Δt t + S 2 Δt ( ΔS ) 2 t = ± 1

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A body travels uniformly a distance of (S + $∆$ S) in a time ( $t \pm Δt$ ). What may be the condition so that body within the error limits move with a velocity $(\frac{S}{t} \pm \frac{ΔS}{Δt})$ ;

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$\frac{Δt}{t} + \frac{S (Δt)^{2}}{(ΔS) t^{2}} = \pm 1$

$\frac{Δt}{t} + \frac{SΔt}{ΔSt} = \pm 1$

$\frac{Δt}{t} + \frac{(ΔS) t}{S (Δt)} = \pm 1$

$\frac{Δt}{t} + \frac{S^{2} Δt}{(ΔS)^{2} t} = \pm 1$

answer is A.

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Detailed Solution

$\begin{array}{l} V = \frac{S}{t} \\ ΔV = \frac{1}{t} \cdot \frac{\partial S}{\partial S} \cdot ΔS + \frac{S}{t^{2}} Δt = (\frac{ΔS}{t} + \frac{SΔt}{t^{2}}) \end{array}$

$\begin{array}{l} So \frac{ΔS}{t} + \frac{SΔt}{t^{2}} = \frac{ΔS}{Δt} \cdot \frac{Δt}{t} + \frac{(ΔS) \cdot S (Δt)^{2}}{(ΔS) \cdot t^{2} (Δt)} \\ or \frac{ΔS}{Δt} [\frac{Δt}{t} + \frac{S (Δt)^{2}}{(ΔS) t^{2}}] = \pm \frac{ΔS}{Δt} (given) \\ or \frac{Δt}{t} + \frac{S (Δt)^{2}}{(ΔS) t^{2}} = \pm 1 \end{array}$