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 intervals with speed 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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If t_{1} and 2t^{2} are the time taken by particle to cover first and second half distance respectively.
\(t_{1} = \frac{x/2}{3} = \frac{x}{6}\) …(i)
x_1 = 4.5 t_2 and x_2 = 7.5 t_2
So, \(X_1 + X_2 = \frac{X}{2} \Rightarrow 4.5 t_2 + 7.5 t_2 = \frac{X}{2}\)
\(t_{2} = \frac{X}{24}\) …(ii)
Total time \(t = t_{1} + 2t_{2} = \frac{x}{6} + 2\frac{x}{12} = \frac{x}{4}\)
So, average speed \(= 4 \, m / sec\) .
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