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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 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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4 m/s

5 m/s

5.5 m/s

4.7 m/s

answer is A.

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Detailed Solution

t₁= $\frac{(\frac{s}{2})}{3}$ = $\frac{s}{6}$
$\frac{s}{2}$ =4.5×t₂+7.5t₃

⇒12t₂= $\frac{s}{2}$ (Given that t₂=t₃)

⇒t₂= $\frac{s}{2 \times 12}$
Therefore, Total time t=t₁+t₂+t₃

= $\frac{s}{6} + \frac{s}{24} + \frac{s}{24}$

= $\frac{s}{4}$
Average of $\frac{s}{t}$ = $\frac{s}{\frac{s}{4}}$ =4m/s

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