A smooth track in the form of a quarter circle of radius \(6\text{ m}\) lies in the vertical plaine (as shown in figure above). A particle of weight \(4N\) moves from \(P_1 \) to \(P_2 \) under the action of forces \(\vec{F_1}, \vec{F_2}, \vec{F_3} \). Force \( \vec{F_1} \) is always towards \(P_2\) and is always \(20N\) in magnitude, force \(\vec{F_2} \) always acts horizontally and is always \(30N\) in magnitude, force \(\vec{F_3} \) always acts tangentially to the track and is of magnitude \((15-10s)N\) when \(s\) is in meters.

If the particle has speed \(4 \text{ m/s} \) at \(P_1\), what will be its speed be at \(P_2 \)? Give your answer in 1 decimal place and in \(\text{ m/s} \). Assume take \(g = 9.8 \text{ m/s}^2 \).

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