A particle moves on a straight line in such a way that it covers first half distance with speed 3m/sec and next half distance in 2 equal time intervals with speed 4.5m/s and 7.5m/s respectively. Find the 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/2) = S/2

T = S/12       ...............4

total time taken during its motion is T+t

Ttotal = T+t = S/12+S/6 = 3S/12=S/4

total distance = S

average speed = total distance/total time =

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