Class 9 > Unit # 02: Kinematics > Free Fall Motion

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Unit No. 2 Kinematics - Free Fall Motion & Motion Under Gravity

Q. Describe Free Fall Motion and Acceleration Due to Gravity

Acceleration Due to Gravity / Free Falling Objects

"Galileo was the first scientist to appreciate that, neglecting the effect of air resistance, all bodies in free-fall close to the Earth's surface accelerate vertically downwards with the same acceleration: namely $9.8\text{ m/s}^2$."

Example

If a ball is thrown vertically upward, it rises to a particular height and then falls back to the ground. However, this is due to the attraction of the earth which pulls the object towards the ground.

Characteristics of Free Falling Bodies

• When a body is thrown vertically upward, its velocity continuously decreases and becomes zero at maximum height. During this motion, the value of acceleration is negative and final velocity is zero ($a = -9.8\text{ m/s}^2$, $v_f = 0$).
• When a body falls back to the ground, its velocity continuously increases and becomes maximum just before hitting the ground. During free fall towards the earth, acceleration is positive and initial velocity from the highest point is zero ($a = 9.8\text{ m/s}^2$, $v_i = 0$).
• Acceleration due to gravity is denoted by $g$ (or $a$) and its standard value near the Earth's surface is $9.8\text{ m/s}^2$.

Equations of Motion for Free-Falling Bodies

Replacing acceleration ($a$) with gravitational acceleration ($g$) and distance ($S$) with height ($h$), the three equations of motion for bodies moving under gravity are:

1. First Equation of Motion under Gravity

$v_f = v_i + gt$

2. Second Equation of Motion under Gravity

$h = v_i t + \frac{1}{2}gt^2$

3. Third Equation of Motion under Gravity

$2gh = v_f^2 - v_i^2 \quad \text{or} \quad v_f^2 - v_i^2 = 2gh$

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