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Two particles A and B start moving simultaneously along the line joining them in the same direction with acceleration of `1 m//s^2 and 2 m//s^2` and speeds `3 m//s and 1 m//s` respectively. Initially, A is 10 m behind B. What is the minimum distance between them? |
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Answer» At minimum distance, their velocities are same, `:. v_A=v_B or u_A+a_At=u_B+a_Bt` or `(3+t)=(1+2t) or t=2s` Minimum distance, `d_(min)`=Initial distance- extra displacement of A upto this instant due to its greater speed `=10-(s_A-s_B)` `=10+s_B-s_A` `=10+(u_Bt+1/2a_Bt^2)-(u_At+1/2a_At^2)` `=10+[(1)(2)+1/2(2)(2)^2]-[(3)(2)+1/2(1)(2)^2]` `=8m` |
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