b
આપેલ અંતર \( s = (13.8 \pm 0.2) m\)  અને સમય \( t = (4.0 \pm 0.3) s\)

વેગ \( \,V  =  \frac{s}{t}\,\, = \,\,\frac{{13.8}}{{4.0}}\,\, = \,\,3.45\,\,m{s^{ - 1}}\,\, = \,\,3.5\,\,m{s^{ - 1}}\)

\(\frac{{\Delta v}}{v}\,\, = \,\, \pm \,\,\left( {\frac{{\Delta s}}{s}\,\, + \,\,\frac{{\Delta t}}{t}} \right)\,\, = \,\, \pm \,\,\left( {\frac{{0.2}}{{13.8}}\,\, + \;\,\frac{{0.3}}{{4.0}}} \right)\)

\( = \,\, \pm \,\,\left( {\frac{{0.8\,\, + \;\,4.14}}{{13.8\,\, \times \,\,4.0}}} \right)\,\, = \,\, \pm \,\,\frac{{4.49}}{{13.8\,\, \times \,\,4.0}}\,\, = \,\, \pm \,\,0.0895\)

\(\Delta \,v  =   \pm 0.0895\,\, \times \,\,v\,\, = \,\, \pm \,\,0.0895\,\, \times \,\,3.45\,\, = \,\, \pm 0.3087\,\, = \,\, \pm \,\,0.31\)

\(\therefore \,\,v  =  \left( {3.5\,\, \pm \,\,0.31} \right)\,m{s^{ - 1}}\,\)

વેગમાં પ્રતિશત ત્રુટિ \( = \,\,\frac{{\Delta v}}{v}\,\, \times \,\,100\,\, = \,\, \pm \,\,0.0895\,\, \times \,\,100\,\, = \,\, \pm \,\,8.95\,\% \,\, = \,\, \pm \,\,9\% \)