A body falls freely towards the earth with

Options

A. uniform speed
B. uniform velocity
C. uniform acceleration
D. none of these

Answer

To solve the question regarding a body falling freely towards the Earth, we need to analyze the motion of the body under the influence of gravity. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Free Fall
When a body falls freely towards the Earth, it is acted upon only by the force of gravity. This means that the only force acting on the body is its weight, which is given by the formula:
\[ W = mg \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

**Hint:** Remember that free fall occurs when the only force acting on an object is gravity.

### Step 2: Analyze Acceleration
In free fall, the body experiences a constant acceleration directed towards the center of the Earth. This acceleration is equal to \( g \). Therefore, we can conclude that:
\[ a = g \]
This means that the acceleration of the body is constant.

**Hint:** Constant acceleration means that the value of acceleration does not change over time.

### Step 3: Examine Velocity and Speed
Initially, when the body is at rest, its initial velocity \( u = 0 \). As the body falls, its velocity increases due to the constant acceleration. The relationship between velocity, acceleration, and time can be expressed as:
\[ v = u + at \]
Since \( u = 0 \), we have:
\[ v = gt \]
This shows that the velocity of the body increases continuously as it falls.

**Hint:** Velocity is a vector quantity that depends on both magnitude and direction.

### Step 4: Determine if Speed and Velocity are Uniform
Since the velocity of the body is increasing as it falls, it cannot be uniform. Uniform speed means that the speed remains constant, which is not the case here because the speed (magnitude of velocity) is increasing.

**Hint:** Uniform speed implies no change in speed over time.

### Step 5: Conclusion on Acceleration
While the speed and velocity of the body are not uniform, the acceleration is constant and directed downwards. Therefore, the correct answer to the question is that the body falls with uniform acceleration.

**Hint:** Uniform acceleration means both magnitude and direction of acceleration remain constant.

### Final Answer
The body falls freely towards the Earth with **uniform acceleration**.