U OL Uycle Two identical trains tak...
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U OL Uycle Two identical trains take 3 sec to pass one another when going in the opposite direction e speed of one is increased by 50 %. Find the time (in sec) one would take to pass the other when going in the same direction at their original speed. The

JEE/Engineering Exams
Physics
Solution
91
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assumptions: speed of 1 st train ( =v ). speed of 2 nd train ( =u ). combined length = total distance travelled = L When going in opposite directions with original speeds, ( v-(-u)=L / 3 ) or ( L=3 v+3 u ) now, When speed of one train is increased by ( 50 % ), and time taken is ( 2.5 mathrm{s} ) so, new speed of 1 ( v^{prime}=v+0.5 v=1.5 v ) so ( 1.5 v+u=L / 2.5 ) or ( L=3.75 v+2.5 u ) by subtracting ( 2 ) from ( 1) ( 0.75 v-0.5 u=0 ) ( 1.5 mathrm{v}=mathrm{u} ) now, we have time = distance travelled / speed as the trains are moving in same direction relative velocity ( =u-v ) so, time taken ( t=L /(u-v) ) now, as ( L=3 v+3 u ) ( s 0,(a s u=1.5 v) ) ( L=3 v+3^{star} 1.5 v=7.5 v ) ( u-v=1.5 v-v=0.5 v ) thus, ( t=7.5 mathrm{v} / 0.5 mathrm{v}=15 mathrm{seconds} )
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