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A body travels uniformly a distance of $(13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3) s$. Its velocity with error limits and percentage error is
$(4.0 \pm 0.31), \pm 8\%$
$(3.5 \pm 0.31), \pm 9\%$
$(5.0 \pm 0.37), \pm 9\%$
$(3.8 \pm 0.34), \pm 7\%$
Solution
$ s = (13.8 \pm 0.2) m$
$ t = (4.0 \pm 0.3) s$
$V = \frac{s}{t}\,\, = \,\,\frac{{13.8}}{{4.0}}\,\, = \,\,3.45\,\,m{s^{ – 1}}\,\, = \,\,3.5\,\,m{s^{ – 1}}$
$\frac{{\Delta v}}{v}\,\, = \,\, \pm \,\,\left( {\frac{{\Delta s}}{s}\,\, + \,\,\frac{{\Delta t}}{t}} \right)\,\, = \,\, \pm \,\,\left( {\frac{{0.2}}{{13.8}}\,\, + \;\,\frac{{0.3}}{{4.0}}} \right)$
$ = \pm \,\,\left( {\frac{{0.8\,\, + \;\,4.14}}{{13.8\,\, \times \,\,4.0}}} \right)\,\, = \,\, \pm \,\,\frac{{4.49}}{{13.8\,\, \times \,\,4.0}}\,\, = \,\, \pm \,\,0.0895$
$\Delta \,v = \pm 0.0895\,\, \times \,\,v\,\, = \,\, \pm \,\,0.0895\,\, \times \,\,3.45\,\, = \,\, \pm 0.3087\,\, = \,\, \pm \,\,0.31$
$v = \left( {3.5\,\, \pm \,\,0.31} \right)\,m{s^{ – 1}}\,$
$\frac{{\Delta v}}{v}\,\, \times \,\,100\,\, = \,\, \pm \,\,0.0895\,\, \times \,\,100\,\, = \,\, \pm \,\,8.95\,\% \,\, = \,\, \pm \,\,9\% $
