Question

A particle moving along a straight line travels one third of the total distance with a speed of
3.0 m/s. The remaining distance is covered with a speed of 4.0 m/s for half the time and 5.0 m/s
for the other half of the time. The average speed during the motion is
(A) 4.0 m/s
(B) 6.0 m/s
(C) 3.8 m/s
(D) 2.4 m/s

Ans. = 3.8m/s​

Answer 1

Explanation:

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