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

 

Rendered by QuickLaTeX.com

 

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 (\(v_o = 0\)).

Exercise

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Uniform Acceleration (Prev Lesson)
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