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Question

A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time interval 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. 5.0 m/s
  3. 5.5 m/s
  4. 4.8 m/s

A
5.0 m/s
B
4.0 m/s
C
5.5 m/s
D
4.8 m/s
Solution
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The correct option is (A) 4.0 m/s

Given,

The particle is covering half of the distance with 3 m/s

Other half distance in two equal time intervals with speed of 4.5 m/s and 7.5 m/s

Let the total distance traveled by the particle is S

So,

Time taken by the particle for the first half distance (t1)

t1=S23=S6

According to the question second half distance is traveled in two equal time time intervals

So,

Let time interval be t

We can write,

S2=4.5×t+7.5t12t=S2

Or, t=S24

Now,
Total time t=t1+t+t=S6+S24+S24=S4
We know,
Averagespeed=TotaldistancetraveledTotaltimetaken
So,
Average = St=SS4=4m/s

Hence, the average speed is 4 m/s

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