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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? ```
7 years ago

510 Points
```										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
```
7 years ago
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