Free fall convention in kinematics If a body falls freely under gravity, which value (with sign) is typically taken for gravitational acceleration g when the downward direction is chosen as positive?

Introduction / Context:
Sign conventions in dynamics are crucial for error-free calculations. This problem asks which signed value of the gravitational acceleration g is taken in free fall when we deliberately choose the downward direction as positive.

Given Data / Assumptions:

• Standard magnitude of gravitational acceleration near Earth's surface is about 9.8 m/s^2.
• Coordinate system is user-defined; here, the downward direction is specified as positive.
• Air resistance is ignored (ideal free fall).

Concept / Approach:
The sign of acceleration depends on the chosen coordinate axis. If downward is positive, gravitational acceleration is +9.8 m/s^2. If upward were taken as positive, the same acceleration would be written as −9.8 m/s^2. The physics does not change; only the algebraic signs do.

Step-by-Step Solution:

Verification / Alternative check:
Take the position equation s = (1/2) g t^2 with s measured positive downward. With g = +9.8, s grows positively as time increases, matching physical intuition for a falling object.

Why Other Options Are Wrong:

• ±8.9 m/s^2: Incorrect magnitude.
• −9.8 m/s^2: Would be correct only if upward were taken as positive.
• +10 m/s^2 (approx.): A useful approximation in mental math, but the question asks for the typical precise value.

Common Pitfalls:
Mixing up sign convention; always define the axis first. The vector points downward physically; assign the sign consistent with your axis.

Final Answer:
+9.8 m/s^2