What is his average speed for the total journey?
A) \[2V\]
B) \[6V\]
C) \[3V\]
D) \[{}^{V}/{}_{2}\]
Correct Answer: A
Solution :
(i) From \[A\] to\[B\], Speed\[=V\] Distance\[=2\pi R\times \frac{{{60}^{o}}}{{{360}^{o}}}=\frac{2\pi R}{6}\] Time\[=\frac{D}{S}=\frac{2\pi R}{6\times V}\] (ii) From \[B\] to\[C\], Speed\[=2V\] Distance\[=2\pi R\times \frac{{{120}^{o}}}{{{360}^{o}}}=\frac{2\pi R}{2}\] (iii) From \[C\] to\[A\], Speed\[=3V\] Distance\[=2\pi R\times \frac{{{180}^{o}}}{{{360}^{o}}}=\frac{2\pi R}{2}\] Time\[=\frac{D}{S}=\frac{2\pi R}{2\times 3V}\] \[\therefore \]Average speed for total journey \[\text{=}\frac{\text{Total}\,\,\text{Distance}}{\text{Total}\,\,\text{Taken}}\]\[=\frac{2\pi R}{\frac{2\pi R}{6V}+\frac{2\pi R}{6V}+\frac{2\pi R}{6V}}\] \[=\frac{2\pi }{\frac{6\pi R}{6V}}=2\,\,V\]
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