F=mg+mv^2/2 eching

$$F = m g + \frac { m v ^ { 2 } } { 2 }$$

g uchun yechish

$$\left\{\begin{matrix}g=-\frac{v^{2}}{2}+\frac{F}{m}\text{, }&m\neq 0\\g\in \mathrm{R}\text{, }&F=0\text{ and }m=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$mg+\frac{mv^{2}}{2}=F$$

Ikkala tarafdan \frac{mv^{2}}{2} ni ayirish.

$$mg=F-\frac{mv^{2}}{2}$$

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$2mg=2F-mv^{2}$$

Ikki tarafini 2m ga bo‘ling.

$$\frac{2mg}{2m}=\frac{2F-mv^{2}}{2m}$$

2m ga bo'lish 2m ga ko'paytirishni bekor qiladi.

$$g=\frac{2F-mv^{2}}{2m}$$

-mv^{2}+2F ni 2m ga bo'lish.

$$g=-\frac{v^{2}}{2}+\frac{F}{m}$$

F uchun yechish

$$F=\frac{m\left(v^{2}+2g\right)}{2}$$