Directions for: The questions consist of two statements each, printed as assertion and reason. While answering these questions you are required to choose any one of the following five responses A. If both the Assertion and the Reason are true and the Reason is a correct explanation of the Assertion. B. If both the Assertion and the Reason are true but the Reason is not a correct explanation of Assertion. C. If the Assertion is true but the Reason is false. D. If both the Assertion and the Reason are false. E. If Assertion is false but Reason is true.
Assertion: The average speed of an object may be equal to arithmetic mean of individual speeds. Reason: Average speeds is equal to total distance travelled per total lime Liken.A) A
B) B
C) C
D) D
E) E
Correct Answer: A
Solution :
When a particle moves with speeds \[{{v}_{1}},{{v}_{2}},{{v}_{3}}\]... during time intervals\[{{t}_{1}},{{t}_{2}},{{t}_{3}}..\]... respectively then total distance travelled \[{{v}_{1}}{{t}_{1}}+{{v}_{2}}{{t}_{2}}+{{v}_{3}}{{t}_{3}}+....\] and total time taken by particle \[={{t}_{1}}+{{t}_{2}}+{{t}_{3}}+....\] Hence, average speed is given by \[{{v}_{av}}=\frac{{{v}_{1}}+{{t}_{1}}+{{v}_{2}}{{t}_{2}}+{{v}_{3}}{{t}_{3}}+....}{{{t}_{1}}+{{t}_{2}}+{{t}_{3}}+....}\] (Let \[{{t}_{1}}={{t}_{2}}={{t}_{3}}.....=t\]) Then, \[{{v}_{av}}=\frac{({{v}_{1}}+{{v}_{2}}+{{v}_{3}}+.....)t}{nt}\] Therefore, average speed is the arithmetic mean of individual speeds.
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