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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 speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

A
4.0 m/s
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B
5.0 m/s
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C
5.5 m/s
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D
4.8 m/s
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Solution

## The correct option is A 4.0 m/s Let total distance =x m and half of distance is travelled in t1 sec. ⇒ v1×t1=x2, v1=3 m/s ⇒3×t1=x2 ∴t1=x6 s Other half of the distance is covered in two equal time intervals i.e t2 and t3 sec. where t2=t3 ⇒Distance travelled in t2 sec+Distance travelled in t3 sec=x2 ∴v2×t2+v3+t3=x2 where, [v2=4.5 m/sv3=7.5 m/s] ⇒4.5×t2+7.5×t2=x2 ⇒t2=t3=x24 s Average Speed=Total Distance travelledTotal time taken vavg=xx6+x24+x24 ∴vavg=x(x4)=4 m/s

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