Question

# A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of the distance is covered in two equal time intervals with uniform speeds of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

A
1 m/s
B
2 m/s
C
3 m/s
D
4 m/s
Solution
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#### Lets consider, x= total distance covered by a particleHalf of the distance is covered with speed 3m/s, then time required to covered the distance is t1=x6secOther half of the distance is covered in two equal time interval with uniform speed 4.5m/s and 7.5m/s respectivelyThen time required ist2=x4×4.5=x18secAnd t3=x4×7.5=x30secTotal time required , t=t1+t2+t3The average speed of the particle during the motion isvavg=TotaldistancecoveredTotaltimevavg=xtvavg=xt1+t2+t3vavg=xx6+x18+x30vavg=x0.25xvavg=4m/sThe correct option is D.

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