A) \[\frac{3}{8}m{{s}^{-1}}\]
B) \[\frac{8}{3}m{{s}^{-1}}\]
C) \[\frac{4}{3}m{{s}^{-1}}\]
D) \[\frac{16}{3}m{{s}^{-1}}\]
Correct Answer: B
Solution :
Let the total distance travelled by the body is 2S. If \[{{t}_{1}}\]is the time taken by the body to travel first half of the distance, then\[{{t}_{1}}=\frac{S}{2}\] Let \[{{t}_{2}}\] be the time taken by the body for each time interval for the remaining half journey. \[\therefore \] \[S=3{{t}_{2}}+5{{t}_{2}}=8{{t}_{2}}\] So, average speed\[=\frac{\text{Total distance travelled}}{\text{Total}\,\text{time}\,\text{taken}}\] \[=\frac{2S}{{{t}_{1}}+2{{t}_{2}}}\] \[=\frac{2S}{\frac{S}{2}+\frac{S}{4}}\] \[=\frac{8}{3}m{{s}^{-1}}\]
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