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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
  1. 4.0 m/s 
  2. 5.5 m/s
  3. 4.8 m/s
  4. 5.0 m/s


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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