Question

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

• A. $\frac{\Delta t}{t}+ \frac{S\left(\Delta t\right)^{2}}{\left(\Delta S\right)t^{2}}=\pm1$
• B. $\frac{\Delta t}{t}+ \frac{S\Delta t2}{\Delta St}=\pm1$
• C. $\frac{\Delta t}{t}+ \frac{\left(\Delta S\right)t}{S\left(\Delta t\right)}=\pm1$
• D. $\frac{\Delta t}{t}+ \frac{S^{2} \Delta t}{\left(\Delta S\right)^{2} t}=\pm1$

Answer 1

Answer: (A)

$V =\frac{S}{t}$
$\Delta V =\frac{1}{t} .\frac{\partial S}{\partial S}. \Delta S +\frac{S}{t^{2}}\Delta t =\left(\frac{\Delta S}{t}+\frac{S\Delta t}{t^{2}}\right)$
So $\frac {\Delta S}{t} + \frac{S \Delta t}{t^{2}} =\frac{ \Delta S}{\Delta t} .\frac{\Delta t}{t} +\frac{(\Delta S) .S(\Delta t)^{2}}{(\Delta S).t^{2} (\Delta t)}$
or $\frac{\Delta S}{\Delta t} [\frac{\Delta t}{t}+\frac{S(\Delta t)^{2}}{(\Delta S)t^{2}}] =\pm \frac {\Delta S}{\Delta t}$ (given)
So, $\frac{\Delta t}{t} +\frac{S(\Delta t)^{2}}{(\Delta S)t^{2}} = \pm 1$