In kinematics, the motion of a freely falling body near the earth (neglecting air resistance) is an example of which type of accelerated motion?

Introduction / Context:
When an object is released from rest and allowed to fall freely under gravity near the earth's surface, its speed increases as it falls. This is a classic example in kinematics and dynamics used to illustrate the concept of acceleration. The question asks you to classify this motion as uniformly or non uniformly accelerated. Understanding this example helps in solving many numerical problems related to free fall, projectile motion, and gravitational effects.

Given Data / Assumptions:

• The body is freely falling near the earth's surface.
• Air resistance is neglected to simplify the analysis.
• The acceleration due to gravity is treated as constant and equal to g.
• We focus on motion in one dimension, vertically downward.

Concept / Approach:
Acceleration is defined as the rate of change of velocity with respect to time. If this rate is constant, the motion is called uniformly accelerated. Near the earth's surface, the acceleration due to gravity g has a nearly constant value, approximately 9.8 metres per second squared, directed downward. When air resistance is negligible, this constant acceleration acts on the falling body throughout its motion, so its velocity increases linearly with time. Therefore, the motion of a freely falling body is uniformly accelerated motion, not non uniform or special variable acceleration.

Step-by-Step Solution:
Step 1: Recall that for free fall near the earth, the only significant force on the body is its weight, equal to mass multiplied by gravitational acceleration g.Step 2: This constant force produces a constant acceleration g, independent of the body's mass.Step 3: In uniformly accelerated motion, acceleration remains the same at all instants of time.Step 4: Since the acceleration due to gravity is taken as constant in this idealised situation, the falling body experiences uniform acceleration.Step 5: Conclude that the motion is uniformly accelerated motion, matching standard kinematics equations such as v = u + g * t and s = u * t + (1 / 2) * g * t^2.

Verification / Alternative check:
You can use experimental or textbook graphs to verify this. A velocity time graph for a freely falling body, neglecting air resistance, is a straight line with slope equal to g, indicating constant acceleration. The displacement time relation forms a parabola, consistent with uniform acceleration. Additionally, many standard kinematics formulas for free fall assume constant acceleration and are derived under that assumption. If acceleration were non uniform, those equations would not hold, and the graphs would look different, which they do not in the ideal case.

Why Other Options Are Wrong:
Non uniformly accelerated motion, option A, refers to situations where acceleration varies with time or position, such as motion with air resistance or changing forces, which is not assumed here. Option C mentions unique accelerated motion with variable direction, which might apply to circular or more complex motion but not to straight downward free fall. Option D, special motion without acceleration, is incorrect because the body clearly speeds up, indicating non zero acceleration. Only option B correctly identifies free fall (without air resistance) as uniformly accelerated motion.

Common Pitfalls:
Students sometimes think that because the speed is changing, the acceleration must also be changing, which is not true. A constant acceleration can still produce changing velocity; in fact, that is its defining feature. Another pitfall is to confuse real life falling, where air resistance plays a role and acceleration decreases over time, with the idealised free fall model used in basic physics. Always pay attention to phrases like neglecting air resistance or in vacuum, which indicate that you should use the constant acceleration model for gravity.

Final Answer:
Uniformly accelerated motion