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Motion in A Straight Line question

2007 · Q130
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Motion in A Straight Line question

2007 · Q130

NEETPhysicsMotion in A Straight LineMCQ+4 / −1
A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is
  1. A
    vuvd\sqrt {{v_u}{v_d}}vu​vd​​
  2. B
    vdvuvd+vu{{{v_d}{v_u}} \over {{v_d} + {v_u}}}vd​+vu​vd​vu​​
  3. C
    vu+vd2{{{v_u} + {v_d}} \over 2}2vu​+vd​​
  4. D
    2vdvuvd+vu{{2{v_d}{v_u}} \over {{v_d} + {v_u}}}vd​+vu​2vd​vu​​
View written solutionFree

Correct answer: D

Let total distance = 2S

Let car take t1 time to cover first S distance from X to Y,

∴\therefore∴ t1 = Svu{S \over {{v_u}}}vu​S​

Let car take t2 time to cover S distance,from Y to X,

∴\therefore∴ t2 = Svd{S \over {{v_d}}}vd​S​

∴\therefore∴ Average speed = 2SSvu+Svd{{2S} \over {{S \over {{v_u}}} + {S \over {{v_d}}}}}vu​S​+vd​S​2S​ = 2vuvdvu+vd{{2{v_u}{v_d}} \over {{v_u} + {v_d}}}vu​+vd​2vu​vd​​

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