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

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Answer & Solution

Correct Answer

(D) \(8 \mathrm{~m} / \mathrm{s}\)

Step-by-step Solution

Detailed explanation

\(B D \Rightarrow S=9 t+15 t=24 t\)

\(A B \Rightarrow S=6 t_1=24 t \Rightarrow t_1=4 t\)

\(<\text { speed }>=\frac{\text { dist. }}{\text { time }}=\frac{48 t}{2 t+t_1}\)

\(=\frac{48 t}{2 t+4 t} \Rightarrow \frac{48 t}{6 t} \Rightarrow 8 \mathrm{~m} / \mathrm{s}\)

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