question_answer

A car travels along the four sides of a square at speeds v, 2v, 3v, 4v respectively. If u is the average speed of the car in its travel around the square, then which one of the following is correct?

A) \[u=2.25v\]                   

B) \[u=3v\]

C) \[u<u<2v\]       

D) \[3v<u<4v\]

Correct Answer: C

Solution :

Let side of a square be x To cover x, distance in a side AB, times will be  \[=\frac{x}{v}\] Similarly, To cover x distance in a side BC, times will be \[=\frac{x}{2v}\] To cover x. distance in, a side CD, time will be \[=\frac{x}{3v}\] And to cover x, distance in a side DA, time will be \[=\frac{x}{4v}\] \[\because \]\[\text{Average speed}\,\text{(u)=}\frac{\text{Total distance}}{\text{ }\!\!~\!\!\text{ Total time}}\] \[=\frac{(x+x+x+x)}{\frac{x}{v}+\frac{x}{2v}+\frac{x}{3v}+\frac{x}{4v}}\] \[=\frac{48v}{25}\] \[=1.92\,v\] Which lies in the interval \[v<u<2v.\]