question_answer

The speedometer of a car moving eastward reads \[50\,km/h\]. It passes another car which travels westward at 50 km/h. (i) Do both the cars have same speed? (ii) Do they have the same velocity? (iii) What is the relative velocity of car A w.r.t. car B.

Answer:

                Time taken by person to travel first half length, \[{{t}_{1}}=\frac{\left( d/2 \right)}{{{\upsilon }_{1}}}=\frac{d}{2{{\upsilon }_{1}}}\] Time taken by person to travel second half length, \[{{t}_{2}}=\frac{d/2}{{{\upsilon }_{2}}}=\frac{d}{2{{\upsilon }_{2}}}\] \[\therefore \]                  Total time = \[{{t}_{1}}+{{t}_{2}}=\frac{d}{2}\left[ \frac{1}{{{\upsilon }_{1}}}+\frac{1}{{{\upsilon }_{2}}} \right]=\frac{d\left( {{\upsilon }_{1}}+{{\upsilon }_{2}} \right)}{2{{\upsilon }_{1}}{{\upsilon }_{2}}}\] \[\therefore \]  Mean velocity or average velocity \[=\frac{d}{{{t}_{1}}+{{t}_{2}}}=\frac{2{{\upsilon }_{1}}{{\upsilon }_{2}}}{\left( {{\upsilon }_{1}}+{{\upsilon }_{2}} \right)}\]