question_answer

A person travelling on a straight line moves with a uniform velocity\[{{v}_{1}}\] for some time and with uniform velocity\[{{v}_{2}}\] for the next equal time. Find the average velocity

Answer:

\[Average\,velocity=\frac{total\,\,displacement}{total\,time\,\,taken}\] \[{{V}_{ave}}=\frac{{{s}_{1}}+{{s}_{2}}}{{{t}_{1}}+{{t}_{2}}}\] \[{{s}_{1}}={{v}_{1}}{{t}_{1}}\,\,\And \,\,{{s}_{2}}={{v}_{2}}{{t}_{2}}\,\,\sin ce\,\,t={{t}_{1}}={{t}_{1}}\] \[{{v}_{ave}}=\frac{{{v}_{1}}t+{{v}_{2}}t}{t+t}=\frac{[{{v}_{1}}+{{v}_{2}}]}{2t}=\frac{{{v}_{1}}+{{v}_{2}}}{2}\]