InterviewSolution
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InterviewSolution
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A particle travels along a straight line. It covers halg the distance with a speed (v). The remaining part of the distance was covere with speed `v_(1)` for half the time and with speed `v_(2)` for the other half the time . Find the average speed of the particle over the entire motion. |
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Answer» Let (S) be the total distance to betravelled by the particle. Time taken by particle to travel halgf the distance `(S//2)` is `t_(1) =(S//2)/v =S/(2v)` Let `2t_(2)` be the time takenby particle to cover the remainig distance `S//2` Distance travelled by particle in time `t_(2)` while travelling with speed `v_(1)` is Distance travelled by particle in time `t_(2)` while travelling with speed `v_(2` is `S_(2) =v_(1) t_(2)` `S_(1) +S_(2) =v_(1) t_(2) + v_(2) t_(2) ` But `S_(1) +S_(2) =S/2 =v_(1) t_(2) +v_(2) t_(2) + (v_(1) +v_(2)) t_(2)` or `2t_(2) =S/((v_(1) +v_(2))` Average speed `=(total distance travelled)/(total time talke)` `=S/(t_(1) +2t_(2)) =S/((S//2 v) + S//(v_(1) +v_(2))` `=(2 v(v_(1) + v_(2))/(v_(1) +v_(2) +2v)`. |
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