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Somewhere in a reference book I read about escape speed of a particle for earth.

Let a particle is projected from the Earth surface. Let its mass be m and speed of projection be u. Let mass of Earth be M and its radius be R.

According to law of conservation of energy,

https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-prn2/q86/s720x720/1175485_1407193806174392_209657781_n.jpg

https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn2/q88/s720x720/1236159_1407193812841058_1152852378_n.jpg

The problem is that,

If the Ist term becomes negative also but its magnitude is less than the IInd term, then also final Kinetic energy will be positive. And the particle will never doesn't give the proper answer. Friend isn't it so?

Please help me in understanding this.

Thank you all in advance.