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Two particles A and B start fro rest and move for equal time on a straight line. The particle A has an acceleration a for first half of time and 2a for the second half. The particle B has an acceleration 2a for the second half. The particle B has an acceleration 2a for the first half and a for the second half. Which particle has covered larger distance?


Two particles A and B start fro rest and move for equal time on a straight line. The particle A has an acceleration a for first half of time and 2a for the second half. The particle B has an acceleration 2a for the second half. The particle B has an acceleration 2a for the first half and a for the second half. Which particle has covered larger distance?

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

particle A ( accleration a for first half and 2a for second half)

particle B ( accleration 2a for first half and a for second half)

let the total time for complete journey be T

for particle A

     for first half  time (T/2 , accleration a)

                                       S1=ut+at^2/2       (u=0)

                                      S1=aT^2/8....1

now particle has gained some velocity

      v=u+at

       v=aT/2

       for second half time (T/2 ,accleration 2a)

  S2=ut+2at^2/2

     S2=aT^2/2.........2

     S=S1+S2=5aT^2/8   .............1( total distance moved for particle A )

for particle B

  for first half t=T/2 ,accleration=2a

             S1=Ut+2at^2/2       (u=0)

              S1=aT^2/4

 now the particle is having velocity

         v=u+2at=2aT/2=aT

 for second half  t=T/2 ,accleration =a

              S2  =ut+at^2/2

                    =aT.T/2 + aT^2/8

                   =5aT^2/8

  S=S1+S2=7aT^2/8...............3 (total distance moved for particle B)

 so distance moved by B particle is greater

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