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A particle moves on a straight line in such a way it covers 1st half distance with speed 3m/s and next half distance in two equal time intervals with speed 4.5m/s and 7.5m/s respectively. Find average speed of the particle.
 let total distance of path is S ...   for first half , time taken if t speed = distance/time 3 = S/2t t = S/6     .............1   for second half , time taken is T ... for first T/2 it moves with 4.5 speed = distance/time 4.5 = 2x/T  x = 4.5T/2  ...........2 for second T/2 it moves with 7.5 7.5 = 2y/T y = 7.5T/2      ..........3 we have , x+y = S/2so (7.5+4.5)T = S/2 T = S/24       ...............4 total time taken during its motion is T+t  Ttotal = T+t = S/24+S/6 = 5S/24 total distance = S average speed = total distance/total time = S/5S/24 = 24/5 = 4.8m/s
let total distance of path is S ...
Â
for first half , time taken if t
speed = distance/time
3 = S/2t
t = S/6Â Â Â Â Â .............1
for second half , time taken is T ...
for first T/2 it moves with 4.5
4.5 = 2x/T
 x = 4.5T/2  ...........2
for second T/2 it moves with 7.5
7.5 = 2y/T
y = 7.5T/2Â Â Â Â Â Â ..........3
we have , x+y = S/2so
(7.5+4.5)T = S/2
T = S/24Â Â Â Â Â Â Â ...............4
total time taken during its motion is T+t
 Ttotal = T+t = S/24+S/6 = 5S/24
total distance = S
average speed = total distance/total time = S/5S/24 = 24/5 = 4.8m/s
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