A) 4.0 m/s
B) 5.0 m/s
C) 5.5 m/s
D) 4.8 m/s
Correct Answer: A
Solution :
[a] If \[{{t}_{2}}\]and \[2{{t}_{2}}\] are the time taken by particle to cover first and second half distance, respectively, then \[{{t}_{1}}=\frac{x/2}{3}=\frac{x}{6}\] \[{{x}_{1}}=4.5{{t}_{2}}\] and \[{{x}_{2}}=7.5{{t}_{2}}\] So, \[{{x}_{1}}={{x}_{2}}=\frac{x}{2}\Rightarrow 4.5{{t}_{2}}+7.5{{t}_{2}}=\frac{x}{2}\] \[{{t}_{2}}=-\frac{x}{24}\] Total time \[{{t}_{1}}+{{x}_{2}}+2{{t}_{2}}=\frac{x}{6}+\frac{x}{12}=\frac{x}{4}\] So, average speed 4 m/sec.
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