# 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?

509 Points
11 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