Question

A particle travels half of the distance of a straight journey with speed $6m/s$. The remaining part of the 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:

• A. $3m/s$
• B. $4m/s$
• C. $\frac{3}{4}m/s$
• D. $5m/s$

Answer 1

The correct option is B $4m/s$

Let the total distance be d.

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

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

The times of second and third parts of the journey are equal $t_2=t_3$. The sum of distances of these

parts are $\frac{d}{2}$ Let the distance of the second part of the journey be $x$. Then

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

$t_2=\frac{\frac{d}{6}}{2}=\frac{d}{12}=t_3$

Total time of journey:

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

Average Speed:

$V=\frac{d}{t}=4m/s$