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>> $A particle moving in a straight line cov$

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

A

$4.0 m / s$

B

$5.0 m / s$

C

$5.5 m / s$

D

$4.8 m / s$

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Solution

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Correct option is A)

$t_{1} = \frac{\frac{S}{2}}{3} = \frac{S}{6}$
$\frac{S}{2} = 4.5 \times t_{2} + 7.5 t_{3} \Rightarrow 12 t_{2} = \frac{S}{2}$
We have $t_{2} = t_{3}$
Total time $t = t_{1} + t_{2} + t_{3} = \frac{S}{6} + \frac{S}{2 4} + \frac{S}{2 4} = \frac{S}{4}$
Average of $\frac{S}{t} = \frac{S}{\frac{S}{4}} = 4 m / s$

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