The motion of a freely falling body near the Earth surface (neglecting air resistance) is an example of which type of motion?

Introduction / Context:
Freely falling bodies, such as an object dropped from a height near the Earth surface, are standard examples used in kinematics and dynamics. When air resistance is neglected, their motion is governed almost entirely by gravity, which produces a constant acceleration. Recognising the type of motion helps in applying the correct equations of motion. This question asks you to classify the motion of such a freely falling object.

Given Data / Assumptions:

• The body is falling freely under gravity near the Earth surface.
• Air resistance and other forces are neglected.
• The acceleration due to gravity g is taken as constant in magnitude and direction.
• We are considering motion along a straight vertical line.

Concept / Approach:
Uniformly accelerated motion is defined as motion in which the acceleration remains constant in magnitude and direction. For a freely falling body near the Earth surface and over moderate height ranges, the gravitational field can be treated as uniform, giving a constant acceleration g downward. Therefore, the velocity of the body changes at a constant rate, making the motion uniformly accelerated. Non uniform acceleration would involve changing acceleration, and constant velocity motion requires zero acceleration, which does not match the situation of a falling object.

Step-by-Step Solution:
Step 1: Recognise that the only significant force acting on a freely falling body, in the absence of air resistance, is its weight, given by m * g. Step 2: By Newton second law, the acceleration a of the body is F / m = (m * g) / m = g, which is constant in magnitude and directed downward. Step 3: Since acceleration is constant, the velocity of the body changes linearly with time, and displacement follows the standard equations of uniformly accelerated motion, such as v = u + a * t and s = u * t + (1 / 2) * a * t^2. Step 4: Because acceleration is constant and non zero, the motion is not with constant velocity or constant speed. Step 5: Therefore, the motion of the freely falling body is an example of uniformly accelerated motion.

Verification / Alternative check:
Experimental measurements of falling objects over small height ranges show that the time of fall and distance satisfy the relation s proportional to t^2, which is characteristic of constant acceleration motion. If acceleration were non uniform, this relation would not hold. Also, standard kinematics problems treat free fall with a single constant g value, confirming the use of uniformly accelerated motion equations.

Why Other Options Are Wrong:
Non-uniformly accelerated motion: This would mean acceleration changes with time or position, which is not assumed for simple free fall near the Earth surface. Motion with constant velocity: A constant velocity requires zero acceleration, but free fall clearly involves a non zero downward acceleration g. Motion with constant speed in any direction: The speed of a freely falling body increases as it falls, so the speed is not constant.

Common Pitfalls:
Students sometimes confuse uniformly accelerated motion with uniform motion. Uniform motion has constant velocity, while uniformly accelerated motion has constant acceleration but changing velocity. Another source of confusion is the effect of air resistance; in realistic situations, acceleration may decrease as speed increases, but in introductory physics, air resistance is neglected to highlight the ideal case of constant acceleration g.

Final Answer:
The motion of a freely falling body near the Earth surface (neglecting air resistance) is an example of uniformly accelerated motion.