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Motion in A Straight Line question

2011 · Q107
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Motion in A Straight Line question

2011 · Q107

NEETPhysicsMotion in A Straight LineMCQ+4 / −1
A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is
  1. A
    v1+v22{{{v_1} + {v_2}} \over 2}2v1​+v2​​
  2. B
    v1v2v1+v2{{{v_1}{v_2}} \over {{v_1} + {v_2}}}v1​+v2​v1​v2​​
  3. C
    2v1v2v1+v2{{2{v_1}{v_2}} \over {{v_1} + {v_2}}}v1​+v2​2v1​v2​​
  4. D
    v12v22v12+v22{{v_1^2v_2^2} \over {v_1^2 + v_2^2}}v12​+v22​v12​v22​​
View written solutionFree

Correct answer: C

Let total distance = 2S

Let particle take t1 time to cover first S distance,

∴\therefore∴ t1 = Sv1{S \over {{v_1}}}v1​S​

Let particle take t2 time to cover last S distance,

∴\therefore∴ t2 = Sv2{S \over {{v_2}}}v2​S​

∴\therefore∴ Average speed = 2SSv1+Sv2{{2S} \over {{S \over {{v_1}}} + {S \over {{v_2}}}}}v1​S​+v2​S​2S​ = 2v1v2v1+v2{{2{v_1}{v_2}} \over {{v_1} + {v_2}}}v1​+v2​2v1​v2​​

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