A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed in  of the particle during this motion is
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Answer:
AVERAGE SPEED = 5 m/s
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Let the total distance be 'd'
According to the question:
Case-1:
=>> distance Covered = d/2
=>> speed = 3 m/s
Hence, Time, t = d/2 / 3 ==> t = d/6 ...(1)
Case-2
Time taken = T
T = d/4 / 4.5 + d/4 / 7.5
T = d/18 + d/30
T = 5d + 3d /90
T = 8d / 90
T = 4d / 45
Average Speed = total distance / total time
==> d / ( 4d/45 + d/6 )
==> d / ( 8d + 15d ) /90
==> d / ( 23d / 90)
==> 90d / 23d
==> 90/23
==> 3.91 m/s
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