# A body travelling along a straight line traversed one third of the total distance with velocity 4 m/s. The remaining part of distance was covered with a velocity $2 m/s$ for half the time and with velocity 6 m/s for other half of time. the mean velocity averaged over whole time of motion.

$(a)\; 5 m/s \quad (b)\;4 m/s \quad (c)\;4.5 m/s \quad (d)3.5m/s$

Let total distance 's'
Let time coverd for first one third distance be $t_1$
then $t_1=\large\frac{s/3}{4}=\large\frac{s}{12}$
$t_2$ be time for next two journeys
$\large \frac{2s}{3}$$=2t_2+6 t_2=8t_2$
$t_2=\large\frac{s}{12}$
$average\;velocity=\large\frac{Total\;distane}{Total\;time}$
$\qquad=\large\frac{s}{t_1+2 t_2}$
$\qquad=\large\frac{s}{\Large\frac{s}{12}+\frac{2s}{12}}$
$\qquad=4 m/s$
Hence b is the correct answer

edited Jan 25, 2014 by meena.p