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. $\frac{\Delta t}{t}+\frac{S{\left(\Delta t\right)}^2}{\left(\Delta S\right)t^2}=\pm 1$
• B. $\frac{\Delta t}{t}+\frac{S\Delta t2}{\Delta St}=\pm 1$
• C. $\frac{\Delta t}{t}+\frac{\left(\Delta S\right)t}{S\left(\Delta t\right)}=\pm 1$
• D. $\frac{\Delta t}{t}+\frac{S^2\Delta t}{{\left(\Delta S\right)}^{2}t}=\pm 1$

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, $\frac{\Delta t}{t}+\frac{S(\Delta t{)}^2}{(\Delta S)t^2}=\pm 1$