Question

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

• A. 5
• B. 4
• C. 0
• D. 2

Answer 1

The correct option is B

4

Let total distance = s

Let the time taken to cover first one third distance = $t_1$ , then

$t_1$ = $\frac{\frac{s}{3}}{4}$ = $\frac{s}{12}$

New let $t_2$ be the time for the rest two journeys. Then

$\frac{2s}{3}$ = 2$t_2$ + 6 $t_2$ = 8$t_2$

$\therefore$ = $\frac{2s}{24}$ = $\frac{s}{12}$

$\therefore$ Average velocity = $\frac{totaldisplacement}{totaltime}$

= $\frac{s}{t_1+2t_2}$ = $\frac{s}{\frac{s}{12}+\frac{s}{6}}$ = $\frac{12\times 6}{12+6}$ = 4 m/s