A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is

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Solution

Q.
A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is [2024]

1 8.8 m/s

2 10 m/s

3 9.2 m/s

4 8 m/s

Ans.
(4)

$B C \Rightarrow s = 9 t + 15 t = 24 t$

$A C \Rightarrow s = 6 t_{1} = 24 t \Rightarrow t_{1} = 4 t$

$v_{av} = \frac{dist.}{time} = \frac{48 t}{2 t + t_{1}}$

$\Rightarrow v_{av} = \frac{48 t}{2 t + 4 t} \Rightarrow \frac{48 t}{6 t} \Rightarrow 8 m/s$

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