# Kinematics

### Vertical Motion

###### Vertical Motion

Vertical motion is uniform acceleration, which the acceleration is gravitational acceleration. Since gravitational acceleration has downward direction, then $$a = -g$$.

##### A. FORMULA

\begin{equation*} \begin{array} {lll} h & = h_\text{o} + v_\text{o} \:.\: t - \frac{1}{2} \:.\: g \:.\: t^2 \quad & (1) \\\\ v_\text{t} & = v_\text{o} - g \:.\: t \quad & (2) \\\\ v_\text{t}^2 & = v_\text{o}^2 - 2 \:.\: g \:.\: (h - h_\text{o}) \quad & (3) \end{array} \end{equation*}

• $$h_o$$ = initial position (m)
• $$h$$ = final position (m)
• $$v_o$$ = initial velocity (m/s)
• $$v_t$$ = final velocity (m/s)
• $$g$$ = acceleration (m/s2)
• $$t$$ = time (s)

##### B. GRAPH

A stone is thrown upward from ground and then fall back to the ground. The graph is shown below:

Velocity vs time

Velocity is a vector, so it has positive value when the stone moves upward and negative value when the stone moves downward.

##### C. Free Fall

When a stone moves free fall, it has no initial velocity ($$v_o = 0$$).