h=1/2gt^2+Vt eching

$$h = \frac { 1 } { 2 } g t ^ { 2 } + V t$$

V uchun yechish

$$\left\{\begin{matrix}V=-\frac{gt}{2}+\frac{h}{t}\text{, }&t\neq 0\\V\in \mathrm{R}\text{, }&h=0\text{ and }t=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1}{2}gt^{2}+Vt=h$$

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

$$Vt=h-\frac{1}{2}gt^{2}$$

Tenglama standart shaklda.

$$tV=-\frac{gt^{2}}{2}+h$$

Ikki tarafini t ga bo‘ling.

$$\frac{tV}{t}=\frac{-\frac{gt^{2}}{2}+h}{t}$$

t ga bo'lish t ga ko'paytirishni bekor qiladi.

$$V=\frac{-\frac{gt^{2}}{2}+h}{t}$$

h-\frac{gt^{2}}{2} ni t ga bo'lish.

$$V=-\frac{gt}{2}+\frac{h}{t}$$

g uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1}{2}gt^{2}+Vt=h$$

Ikkala tarafdan Vt ni ayirish.

$$\frac{1}{2}gt^{2}=h-Vt$$

Tenglama standart shaklda.

$$\frac{t^{2}}{2}g=h-Vt$$

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

$$\frac{2\times \frac{t^{2}}{2}g}{t^{2}}=\frac{2\left(h-Vt\right)}{t^{2}}$$

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

$$g=\frac{2\left(h-Vt\right)}{t^{2}}$$