For a uniformly accelerated motion, the average acceleration is equal to

Options

A. unity
B. negative
C. zero
D. uniform acceleration

Explanation

To solve the question regarding the average acceleration in uniformly accelerated motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Average Acceleration**:
Average acceleration is defined as the change in velocity divided by the time taken for that change. Mathematically, it can be expressed as:
\[ a_{avg} = \frac{V_f - V_i}{t} \]
where \( V_f \) is the final velocity, \( V_i \) is the initial velocity, and \( t \) is the time taken.

2. **Using the First Equation of Motion**:
According to the first equation of motion, we have:
\[ V_f = V_i + a \cdot t \]
Here, \( a \) represents the uniform acceleration.

3. **Rearranging the Equation**:
From the first equation of motion, we can rearrange it to find the change in velocity:
\[ V_f - V_i = a \cdot t \]

4. **Substituting into the Average Acceleration Formula**:
Now, we can substitute \( V_f - V_i \) from the rearranged equation into the average acceleration formula:
\[ a_{avg} = \frac{a \cdot t}{t} \]

5. **Simplifying the Expression**:
When we simplify the expression, the time \( t \) cancels out:
\[ a_{avg} = a \]
This shows that the average acceleration for uniformly accelerated motion is equal to the uniform acceleration.

6. **Conclusion**:
Therefore, for uniformly accelerated motion, the average acceleration is equal to the uniform acceleration \( a \).

### Final Answer:
The average acceleration for uniformly accelerated motion is equal to the uniform acceleration \( a \).

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