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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

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Solution

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Half of the distance is covered with speed 3m/s, then time required to covered the distance is

t1=x6sec

Other half of the distance is covered in two equal time interval with uniform speed 4.5m/s and 7.5m/s respectively

Then time required is

t2=x4×4.5=x18sec

And t3=x4×7.5=x30sec

Total time required , t=t1+t2+t3

The average speed of the particle during the motion is

vavg=TotaldistancecoveredTotaltime

vavg=xt

vavg=xt1+t2+t3

vavg=xx6+x18+x30

vavg=x0.25x

vavg=4m/s

The correct option is D.

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