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# A train stopping at two stations 4km apart takes 4 minute on the journey from one of the station to the other. Assuming that it first accelerates with a uniform acceleration x and then that of uniform retardation y. prove that 1/x+ 1/y = 2

Arun Kumar IIT Delhi
`$\\s_1=((1/2)*xt_1^2) \\s_2=(xt_1)^2/2y \\s_1+s_2=4km \\t_2=xt_1/y \\t_1+t_2=4min \\solving\,expression\,1/x+1/y=(t_1+t_2)/(yt_2)=4/yt_2$$\\s_1+s_2=4 \\=>(1/2)xt_1^2+(1/2)(xy)^2/y=4 \\=>t_1t_2(x+y)=8 \\again\,x+y=x+t_1x/t_2=4*x/t_2 \\putting \,in \,the \,equation \\=>4x/t_2*t_1t_2=8 \\=>xt_1=2=y t_2 \\putting \,this \,in\, the\, first \, we\, get\, the\, required \,expression$Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty`