Whakaoti i te s=1/2gt^2+v_{0}tquadd

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

Whakaoti mō d (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te \frac{1}{2}gt^{2} mai i ngā taha e rua.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te v_{0}t.

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

Mā te whakawehe ki te v_{0}t ka wetekia te whakareanga ki te v_{0}t.

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

Whakaoti mō g (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te v_{0}td mai i ngā taha e rua.

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

Whakaraupapatia anō ngā kīanga tau.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te \frac{1}{2}t^{2}.

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

Mā te whakawehe ki te \frac{1}{2}t^{2} ka wetekia te whakareanga ki te \frac{1}{2}t^{2}.

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

Whakaoti mō d

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te \frac{1}{2}gt^{2} mai i ngā taha e rua.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te v_{0}t.

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

Mā te whakawehe ki te v_{0}t ka wetekia te whakareanga ki te v_{0}t.

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

Whakaoti mō g

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te v_{0}td mai i ngā taha e rua.

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

Whakaraupapatia anō ngā kīanga tau.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te \frac{1}{2}t^{2}.

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

Mā te whakawehe ki te \frac{1}{2}t^{2} ka wetekia te whakareanga ki te \frac{1}{2}t^{2}.

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