Question

A particle travels half of the time with constant speed $2m/s$. In remaining half of the time if travels, $\frac{1}{4}th$ distance with constant speed of $4m/s$ and $\frac{3}{4}th$ distance with $6m/s$. Find average speed during the complete journey.

Answer 1

$d=2\times \frac{t}{2}=t$

$\begin{array}{c}\frac{1}{4}d=4t_1\\ d=16t_1\\ \frac{3}{4}d=6\times \left(\frac{t}{2}-t_1\right)\\ \Rightarrow \frac{3}{4}\times 16t_1=3t-6t_1\\ 12t_1+6t_1=3t\\ t_1=\frac{3}{18}t=\frac{t}{6}\\ d=16\times \frac{t}{6}\\ d=\frac{8}{3}t\\ \Rightarrow t=\frac{3d}{8}\\ v_{av}=\frac{Totaldis\tan ce}{Totaltime}=\frac{t+\frac{8t}{3}}{t}=\frac{11}{3}m/s\end{array}$