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Home / Doubts and Solutions/JEE/Mathematics

Ques 38

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Asked by rbhatt16 10th July 2018, 11:46 PM
Answered by Expert
Answer:
Let First part of travel time is t1 with acceleration f
 
since the body starts from rest, speed v1 after time t1 is given by,   v1 = f×t1 ...........(1)
 
distance s1 travelled,  s1 = (1/2)f×t12 .........................(2)
 
Let t2 be the time for second part with retardation r
 
in second part initial speed is f×t1 and comes to rest due to retardation r in time t2 . 
 
hence  t2 = ( f×t1 ) / r  ..............................(3)
 
distance s2 travelled, s2 = ( f×t1 )×t2 - (1/2)×r×t22  ............(4)
 
let us substitute t2  from (3) in (4) and after simplification we get begin mathsize 12px style s subscript 2 space equals space fraction numerator f squared space t subscript 1 superscript 2 over denominator 2 space r end fraction space...................... left parenthesis 5 right parenthesis end style
using eqns. (2) and (5),  begin mathsize 12px style s subscript 1 space plus space s subscript 2 space equals space s space equals space 1 half f cross times t subscript 1 superscript 2 space plus fraction numerator f squared t subscript 1 superscript 2 over denominator 2 space r end fraction space end style ..................(6)
eqn. (6) is simplified to get t1  as,  begin mathsize 12px style t subscript 1 space equals space square root of fraction numerator 2 space r space s over denominator f open parentheses f plus r close parentheses end fraction end root end style ....................(7)
from eqn.(3) and (7), we write begin mathsize 12px style t subscript 2 space equals space f over r cross times square root of fraction numerator 2 space r space s over denominator f open parentheses f plus r close parentheses end fraction end root space equals space square root of fraction numerator 2 space f space s over denominator r open parentheses f plus r close parentheses end fraction end root end style .................(8)
Total time t is given by, begin mathsize 12px style t space equals space t subscript 1 plus t subscript 2 space equals space square root of fraction numerator 2 space s over denominator open parentheses f plus r close parentheses end fraction end root space open curly brackets square root of r over f end root space plus space square root of f over r end root close curly brackets space equals space square root of 2 s open parentheses 1 over f plus 1 over r close parentheses end root end style
Answered by Expert 11th July 2018, 4:36 PM
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