Understanding Uniformly Accelerated Motion

Uniformly accelerated motion is a type of motion where the velocity of an object changes at a constant rate. This means the acceleration is constant throughout the motion.

Analyzing the Motion Options

Let's examine each option to determine which represents uniformly accelerated motion:

• Resting body: A body at rest has zero velocity and zero acceleration. Since the acceleration is not only constant but also zero, it is technically a special case of constant acceleration, but the velocity is not changing. The term "accelerated motion" implies a non-zero acceleration causing a change in velocity.
• Decelerating body: Deceleration is negative acceleration. If the deceleration is constant, then the body is undergoing uniformly accelerated motion (with a negative acceleration value). However, this option just says "decelerating", which doesn't guarantee the deceleration is uniform (constant).
• Parabolic motion: Parabolic motion, often seen in projectile motion (neglecting air resistance), is motion under the influence of gravity. The path is a parabola, but this describes the trajectory, not necessarily uniform acceleration in all cases. However, in projectile motion under constant gravity, the vertical acceleration is constant, and horizontal acceleration is zero (if no air resistance). The resultant acceleration is constant (equal to gravitational acceleration). So, projectile motion *is* uniformly accelerated motion, but the term "parabolic" describes the path, not the acceleration itself, and not all parabolic paths are necessarily due to constant acceleration (though in standard physics problems, they are). The option "freely falling" is more precise regarding the cause of acceleration.
• Freely falling body: A freely falling body is an object moving under the influence of gravity alone, neglecting air resistance. Near the Earth's surface, the acceleration due to gravity, denoted by $\text{g}$, is approximately constant in magnitude and direction (vertically downwards). Thus, a freely falling body experiences constant acceleration equal to $\text{g}$. This perfectly fits the definition of uniformly accelerated motion.

Why Freely Falling Body Motion is Uniformly Accelerated

When an object is freely falling, the only significant force acting on it is gravity. According to Newton's second law of motion, force is equal to mass times acceleration ($\text{F} = \text{ma}$). The force of gravity is $\text{F}_{\text{g}} = \text{mg}$, where $\text{m}$ is the mass and $\text{g}$ is the acceleration due to gravity.

Setting these equal, we get $\text{ma} = \text{mg}$, which simplifies to $\text{a} = \text{g}$.

Since $\text{g}$ is considered constant near the Earth's surface, the acceleration $\text{a}$ of a freely falling body is constant. Therefore, the motion of a freely falling body is an example of uniformly accelerated motion.

Conclusion

Based on the analysis, the motion of a freely falling body is the clearest and most direct example of uniformly accelerated motion among the given options, assuming ideal conditions (neglecting air resistance).

Revision Table: Types of Motion

Additional Information on Uniformly Accelerated Motion

For uniformly accelerated motion in one dimension, we can use kinematic equations to describe the motion. These equations relate initial velocity ($\text{u}$), final velocity ($\text{v}$), acceleration ($\text{a}$), displacement ($\text{s}$), and time ($\text{t}$).

Key Kinematic Equations:

• $\text{v} = \text{u} + \text{at}$
• $\text{s} = \text{ut} + \frac{1}{2}\text{at}^2$
• $\text{v}^2 = \text{u}^2 + 2\text{as}$
• $\text{s} = \frac{(\text{u} + \text{v})}{2}\text{t}$

These equations are only valid when the acceleration $\text{a}$ is constant.