# Sufficient work done?

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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