ແກ້ x_{0}=v_{0}t+1/2gt^2

$$x _ { 0 } = v _ { 0 } t + \frac { 1 } { 2 } g t ^ { 2 }$$

ແກ້ສຳລັບ g (complex solution)

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

ຂັ້ນຕອນສຳລັບການແກ້ສົມຜົນເສັ້ນຊື່

ສະຫຼັບຂ້າງເພື່ອໃຫ້ພົດຕົວແປທັງໝົດຢູ່ຂ້າງຊ້າຍຂອງເຄື່ອງໝາຍເທົ່າກັບ.

$$v_{0}t+\frac{1}{2}gt^{2}=x_{0}$$

ລົບ v_{0}t ອອກຈາກທັງສອງຂ້າງ.

$$\frac{1}{2}gt^{2}=x_{0}-v_{0}t$$

ສົມຜົນຢູ່ໃນຮູບແບບມາດຕະຖານ.

$$\frac{t^{2}}{2}g=x_{0}-tv_{0}$$

ຫານທັງສອງຂ້າງດ້ວຍ \frac{1}{2}t^{2}.

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

ການຫານດ້ວຍ \frac{1}{2}t^{2} ຈະຍົກເລີກການຄູນດ້ວຍ \frac{1}{2}t^{2}.

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

ແກ້ສຳລັບ g

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

ຂັ້ນຕອນສຳລັບການແກ້ສົມຜົນເສັ້ນຊື່

ສະຫຼັບຂ້າງເພື່ອໃຫ້ພົດຕົວແປທັງໝົດຢູ່ຂ້າງຊ້າຍຂອງເຄື່ອງໝາຍເທົ່າກັບ.

$$v_{0}t+\frac{1}{2}gt^{2}=x_{0}$$

ລົບ v_{0}t ອອກຈາກທັງສອງຂ້າງ.

$$\frac{1}{2}gt^{2}=x_{0}-v_{0}t$$

ສົມຜົນຢູ່ໃນຮູບແບບມາດຕະຖານ.

$$\frac{t^{2}}{2}g=x_{0}-tv_{0}$$

ຫານທັງສອງຂ້າງດ້ວຍ \frac{1}{2}t^{2}.

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

ການຫານດ້ວຍ \frac{1}{2}t^{2} ຈະຍົກເລີກການຄູນດ້ວຍ \frac{1}{2}t^{2}.

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

ແກ້ສຳລັບ t (complex solution)

$$\left\{\begin{matrix}t=-\frac{\sqrt{2gx_{0}+v_{0}^{2}}+v_{0}}{g}\text{; }t=-\frac{-\sqrt{2gx_{0}+v_{0}^{2}}+v_{0}}{g}\text{, }&g\neq 0\\t=\frac{x_{0}}{v_{0}}\text{, }&g=0\text{ and }v_{0}\neq 0\\t\in \mathrm{C}\text{, }&g=0\text{ and }v_{0}=0\text{ and }x_{0}=0\end{matrix}\right,$$

ແກ້ສຳລັບ t

$$\left\{\begin{matrix}t=-\frac{\sqrt{2gx_{0}+v_{0}^{2}}+v_{0}}{g}\text{; }t=-\frac{-\sqrt{2gx_{0}+v_{0}^{2}}+v_{0}}{g}\text{, }&\left(g>0\text{ or }x_{0}\leq -\frac{v_{0}^{2}}{2g}\right)\text{ and }\left(x_{0}\leq \text{Indeterminate}\text{ or }g\neq 0\right)\text{ and }\left(g<0\text{ or }\left(g\neq 0\text{ and }x_{0}\geq -\frac{v_{0}^{2}}{2g}\right)\right)\\t=\frac{x_{0}}{v_{0}}\text{, }&g=0\text{ and }v_{0}\neq 0\\t\in \mathrm{R}\text{, }&g=0\text{ and }v_{0}=0\text{ and }x_{0}=0\end{matrix}\right,$$