Question

A body travels uniformly a distance of $(13.8 ± 0.2)\, m$ in a time $(4.0 ± 0.3) \,s$. Its velocity with error limits is

• A. $\left(3.5 \pm 0.6\right)\,ms^{-1}$
• B. $\left(3.5 \pm 0.3\right)\,ms^{-1}$
• C. $\left(6.1 \pm 0.6\right)\,ms^{-1}$
• D. $\left(6.1 \pm 0.3\right)\,ms^{-1}$

Answer 1

Answer: (B)

Here, $s=\left(13.8 \pm0.2\right)\,m$, $t=\left(4.0 \pm 0.3\right)\,s$
$\therefore $ veliocity, $v=\frac{s}{t}=\frac{13.8}{4.0}=3.45\,ms^{-1}$
(Rounded off to first place of decimal)
$\therefore \frac{\Delta v}{v}=\frac{\Delta s}{s}+\frac{\Delta t}{t}=\frac{0.2}{13.8}+\frac{0.3}{4.0}$
$=\frac{0.8+4.14}{13.8\times4.0}=\frac{4.94}{13.8 \times 4.0}$
$=0.0865$
or $\Delta v=v\times 0.0865=3.45 \times 0.0865$
$=0.3087$.
$\therefore $ velocity $=\left(3.5 \pm 0.3\right)\,ms^{-1}$.