If the velocity of an object is increasing and changing at a uniform rate then the acceleration of the object is:

Options

A. Positive
B. Zero
C. Negative
D. Not defined

Answer

To solve the question, let's break it down step by step:

### Step 1: Understand the Concept of Acceleration
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, it can be expressed as:
\[ a = \frac{dv}{dt} \]
where \( dv \) is the change in velocity and \( dt \) is the change in time.

**Hint:** Remember that acceleration tells us how quickly the velocity of an object is changing.

### Step 2: Analyze the Given Information
The problem states that the velocity of the object is increasing. This means that the final velocity (\( v \)) is greater than the initial velocity (\( u \)). Therefore, the change in velocity (\( \Delta v \)) can be expressed as:
\[ \Delta v = v - u > 0 \]
This indicates that the object is speeding up.

**Hint:** When velocity increases, the change in velocity is positive.

### Step 3: Consider the Time Interval
The time interval (\( \Delta t \)) during which this change occurs is always positive because time cannot be negative. Thus, we have:
\[ \Delta t > 0 \]

**Hint:** Time is always a positive quantity in physics.

### Step 4: Determine the Sign of Acceleration
Since both \( \Delta v \) is positive and \( \Delta t \) is positive, we can conclude that:
\[ a = \frac{\Delta v}{\Delta t} > 0 \]
This means that the acceleration \( a \) is positive.

**Hint:** A positive acceleration indicates that the object is speeding up.

### Step 5: Conclusion
From the analysis, we can conclude that if the velocity of an object is increasing and changing at a uniform rate, then the acceleration of the object is positive.

**Final Answer:** The acceleration of the object is positive.