s=1/2gt^2+v_{0}tquadd eching

$$s = \frac { 1 } { 2 } g t ^ { 2 } + v _ { 0 } t \quad d$$

d uchun yechish

$$\left\{\begin{matrix}d=\frac{2s-gt^{2}}{2tv_{0}}\text{, }&t\neq 0\text{ and }v_{0}\neq 0\\d\in \mathrm{R}\text{, }&\left(s=0\text{ and }t=0\right)\text{ or }\left(s=\frac{gt^{2}}{2}\text{ and }v_{0}=0\text{ and }t\neq 0\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1}{2}gt^{2}+v_{0}td=s$$

Ikkala tarafdan \frac{1}{2}gt^{2} ni ayirish.

$$v_{0}td=s-\frac{1}{2}gt^{2}$$

Tenglama standart shaklda.

$$tv_{0}d=-\frac{gt^{2}}{2}+s$$

Ikki tarafini v_{0}t ga bo‘ling.

$$\frac{tv_{0}d}{tv_{0}}=\frac{-\frac{gt^{2}}{2}+s}{tv_{0}}$$

v_{0}t ga bo'lish v_{0}t ga ko'paytirishni bekor qiladi.

$$d=\frac{-\frac{gt^{2}}{2}+s}{tv_{0}}$$

g uchun yechish

$$\left\{\begin{matrix}g=-\frac{2\left(dtv_{0}-s\right)}{t^{2}}\text{, }&t\neq 0\\g\in \mathrm{R}\text{, }&s=0\text{ and }t=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1}{2}gt^{2}+v_{0}td=s$$

Ikkala tarafdan v_{0}td ni ayirish.

$$\frac{1}{2}gt^{2}=s-v_{0}td$$

Shartlarni qayta saralash.

$$\frac{1}{2}gt^{2}=s-dtv_{0}$$

Tenglama standart shaklda.

$$\frac{t^{2}}{2}g=s-dtv_{0}$$

Ikki tarafini \frac{1}{2}t^{2} ga bo‘ling.

$$\frac{2\times \frac{t^{2}}{2}g}{t^{2}}=\frac{2\left(s-dtv_{0}\right)}{t^{2}}$$

\frac{1}{2}t^{2} ga bo'lish \frac{1}{2}t^{2} ga ko'paytirishni bekor qiladi.

$$g=\frac{2\left(s-dtv_{0}\right)}{t^{2}}$$