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.
\(\tau_1 - \frac{x}{2 \cdot 3} - \frac{x}{6}\) …(i)
\(x_{1} \quad 4.5 \tau_{2}\) and \(x_2 \quad 7.5\, t_2\)
So, \(\dot{x}_{1} + x_{2} - \frac{x_{1}}{2} = 4.5 t_{2} + 7.5 t_{3} - \frac{x_{1}}{2}\)
\(\tau_{z} = -\frac{x}{2\sqrt{24}}\) …(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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