### Topic Content:

- Motion under Gravity
- Worked Examples

Scientists carried out various research on the motion of objects falling under gravity and were able to come up with an acceptable concept that all bodies falling under gravity freely to the earth moved with the same acceleration irrespective of their masses. This gravitational acceleration is the acceleration of an object caused by the force of gravitation.

Neglecting friction such as air resistance, all bodies accelerate in a gravitational field at the same rate relative to the center of mass.

This acceleration is known as acceleration due to gravity denoted by **g**.

When an object is falling to the earth, it obeys the law of gravity and it is positive g (+g) but when it is an object moving vertically upward, it is against gravity hence, it is denoted as negative g (-g), therefore, for bodies falling freely under gravitational motion, a is replaced by g, hence, the equations of motion for the uniformly accelerated bodies become;

Also note that s is replaced by h, where h is the height of the object above the ground.

v = \( \scriptsize u \pm gt \)

h = \( \scriptsize ut \pm \normalsize \frac{1}{2} \scriptsize gt^2 \)

v^{2} = \( \scriptsize u^2 \pm 2gh \)

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