Question

a particle travels half of the distance of a straight journey with speed 6m/s .the remaining part of distance is covered with speed 2m/s for half of the time of remaining journey and with speed 4m/s for the other half of time .the average speed of the particle is ??????????

Answer 1

A particle travels half of the distance of a straight journey with speed $6\mathrm{m/s}$ . the remaining part of distance is covered with speed $2\mathrm{m/s}$ for half of the time of remaining journey and with speed $4\mathrm{m/s}$ for the other half of time. the average speed of the particle is

Solution

Let the total distance be d.

In the first part of journey particle travels distance $\frac{d}{2}$ with speed $6\mathrm{m/s}$, so corresponding time:

$$t_1 = \frac{d}{\frac{2}{6}} = \frac{d}{12}s.$$

The times of second and third parts of journey are equal $t_2 = t_3$. The sum of distances of these parts are $\frac{d}{2}$. Let the distance of second part of journey be $x$. Then

$$t_2 = t_3 \rightarrow \frac{x}{2} = \frac{\frac{d}{2} - x}{4} \rightarrow x = \frac{d}{6}m,$$ $$t_2 = \frac{d}{\frac{6}{2}} = \frac{d}{12} = t_3.$$

Total time of journey:

$$T = t_1 + t_2 + t_3 = 3\frac{d}{12} = \frac{d}{4}s$$

Average Speed:

$$V = \frac{d}{T} = 4\frac{m}{s}.$$

Answer: $4\frac{m}{s}$.