question_answer

A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. What is the average speed of the particle?

Answer:

\[{{V}_{ave}}=\frac{s}{\frac{s/2}{3}+\frac{s'}{V'}}=\frac{s}{{{t}_{1}}+{{t}_{2}}}\] \[\Rightarrow \frac{s}{2}=4.5\times \frac{{{t}_{2}}}{2}+7.5\times \frac{{{t}_{2}}}{2}\] \[s=12{{t}_{2}}\Rightarrow {{t}_{2}}=\frac{s}{12}\]                           ……..(1) \[{{V}_{ave}}=\frac{s}{\frac{s}{6}+\frac{s}{12}s\left( \frac{1}{6}+\frac{1}{12} \right)}=\frac{1}{\frac{18}{6\times 12}}\]