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.
\(\tau_{1} - \frac{x/2}{3} - \frac{x}{6}\) …(i)
\(x_{1} \quad 4.5 \tau_{2}\) and \(x_{2} \quad 7.5\, t_{2}\)
So, \(x_1 + x_2 - \frac{x}{2} = 4.5 t_2 + 7.5 t_1 - \frac{x}{2}\)
\(\tau_z = -\frac{x}{2\sqrt{3}}\) …(ii)
Total time \(t - t_1 + 2t_2 - \frac{x}{6} + \frac{x}{12} - \frac{x}{4}\)
So, average speed 4 m/s .
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