In free fall problems, handling the gravitational constant $g$ and its signs correctly is crucial.

The value $g = 9.8\text{ m/s}^{2}$ represents the magnitude of gravitational acceleration near Earth's surface. This value is always positive.

Direction Depends on Your Coordinate System

When we choose positive $y$ pointing upward (the standard convention), gravitational acceleration points downward, so:

a_y = -g = -9.8\text{ m/s}^{2}

The negative sign appears because gravity acts opposite to our positive direction.

Kinematic Equations for Free Fall

With upward as positive, the first two kinematic equations become:

v_y = v_{0y} - gt

y = y_0 + v_{0y}t - \frac{1}{2}gt^2

WATCH OUT: Notice we subtract $gt$ and $\frac{1}{2}gt^2$ . A common mistake is writing $a = g$ when using upward as positive—this would incorrectly suggest gravity pulls objects upward!

Interactive Visualization

The object below starts at $y_0 = 20\text{ m}$ with initial upward velocity $v_0 = 15\text{ m/s}$ . Watch how velocity changes sign while acceleration stays constant:

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Free fall

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