За 3 секунды прямолинейного равноускоренного движения тело прошло путь 25 м, увеличив свою скорость в  3 раза. Определи конечную скорость тела.

Для решения этой задачи воспользуемся формулой равноускоренного движения:

S = V0t + (at^2)/2,

где S - пройденный путь, V0 - начальная скорость, t - время движения, a - ускорение.

Из условия задачи известно, что S = 25 м, t = 3 секунды, а скорость увеличилась в 3 раза, то есть V = 3*V0.

Подставим известные значения в формулу:

25 = V03 + (a3^2)/2, V = 3*V0.

Учитывая, что V = 3*V0, подставим это выражение в первое уравнение:

25 = (V/3)3 + (a3^2)/2, 25 = V + 9a/2.

Также у нас есть соотношение между начальной и конечной скоростью:

V = 3*V0.

Подставим это выражение в уравнение 25 = V + 9a/2:

25 = 3V0 + 9a/2, 25 = 3V0 + 9a/2.

Теперь найдем ускорение a:

a = 2*(25 - 3*V0)/9.

Теперь найдем конечную скорость V:

V = 3V0 = 3(V0 + at) = 3(V0 + 2*(25 - 3V0)/93).

V = 3*(V0 + 2*(25 - 3*V0)/9).

Подставим известные значения и найдем конечную скорость тела:

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