At t = 0 , a force F = at 2 is applied to a small body of mass m at an angle α resting on a smooth horizontal plane.

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For breaking off the plane ​ F sin = mg ​ ⇒ at 0 ​ 2 sin α = mg ⇒ t 0 ​ = a sin α mg ​ ​ ​ Speed at time of breaking off. ​ v = ∫ 0 t 0 ​ ​ m at 2 cos α ​ dt = 3 m at 0 2 ​ cos α ​ ​ = 3 m a cos α ​ ⋅ a sin α mg ​ a sin α mg ​ ​ ​ = 9 a tan 2 α sin α mg 3 ​ ​ ​ = m F cos α ​ = m at 0 2 ​ cos α ​ = a sin α amg ​ ⋅ m cos α ​ = g cot α ​ s = ∫ vdt = ∫ 0 t 0 ​ ​ 3 m at 3 ​ cos α dt ​ = 12 m a ​ t 0 2 ​ = 12 m a ​ a 2 sin 2 α m 2 g 2 cos α ​ = 12 a tan α sin α mg 2 ​ ​

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