A particle move with velocity `v_(1)` for time `t_(1) and v_(2)` for time `t_(2)` along a straight line. The magntidue of its average acceleration is

Options

A. `(v_(2)-v_(1))/(t_(1)-t_(2))`
B. `(v_(2)-v_(1))/(t_(1)+t_(2))`
C. `(v_(2)-t_(1))/(t_(2)-t_(1))`
D. `(v_(1)+v_(2))/(t_(1)-t_(2))`

Answer

To find the magnitude of the average acceleration of a particle moving with different velocities over specified time intervals, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Average Acceleration**:
Average acceleration is defined as the change in velocity divided by the total time taken. Mathematically, it is given by:
\[ a_{avg} = \frac{\Delta v}{\Delta t} \]
where \(\Delta v\) is the change in velocity and \(\Delta t\) is the total time.

2. **Identify the Given Variables**:
- Initial velocity \(v_1\) for time \(t_1\)
- Final velocity \(v_2\) for time \(t_2\)

3. **Calculate the Change in Velocity**:
The change in velocity (\(\Delta v\)) can be calculated as:
\[ \Delta v = v_2 - v_1 \]

4. **Calculate the Total Time**:
The total time (\(\Delta t\)) for which the particle is in motion is the sum of the two time intervals:
\[ \Delta t = t_1 + t_2 \]

5. **Substitute into the Average Acceleration Formula**:
Now, substituting \(\Delta v\) and \(\Delta t\) into the average acceleration formula, we get:
\[ a_{avg} = \frac{v_2 - v_1}{t_1 + t_2} \]

6. **Conclusion**:
The magnitude of the average acceleration of the particle is:
\[ |a_{avg}| = \frac{v_2 - v_1}{t_1 + t_2} \]

### Final Answer:
The magnitude of the average acceleration is \(\frac{v_2 - v_1}{t_1 + t_2}\).

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