An object moves with constant acceleration a. Which of the following expressions are also constant?

Options

A. `(d|vecv|)/(dt)`
B. `|(dvecv)/(dt)|`
C. `(d(v^2))/(dt)`
D. `(d(vecv//|vecv|))/(dt)`

Explanation

To solve the question, we need to analyze the situation where an object moves with constant acceleration \( a \). We want to determine which of the following expressions are also constant.

### Step-by-Step Solution:

1. **Understanding Constant Acceleration**:
- Given that the object moves with constant acceleration \( a \), this means that the acceleration does not change over time. Therefore, we can denote the acceleration as \( a = \text{constant} \).

2. **Acceleration and Velocity Relation**:
- The relationship between acceleration \( a \) and velocity \( v \) is given by the equation:
\[ a = \frac{dv}{dt} \]
- This equation indicates that acceleration is the rate of change of velocity with respect to time.

3. **Implications of Constant Acceleration**:
- Since \( a \) is constant, it implies that the change in velocity \( \frac{dv}{dt} \) is also constant. This means that the velocity \( v \) of the object changes linearly with time.

4. **Velocity Expression**:
- If we integrate the acceleration with respect to time, we can express the velocity as:
\[ v(t) = v_0 + at \]
- Here, \( v_0 \) is the initial velocity. From this equation, we see that the velocity \( v \) is not constant; it changes linearly with time due to the constant acceleration.

5. **Magnitude of Velocity**:
- The magnitude of velocity \( |v| \) can also be expressed as:
\[ |v| = |v_0 + at| \]
- Since \( v_0 \) is constant and \( at \) changes with time, the magnitude of velocity \( |v| \) is not constant either.

6. **Conclusion**:
- The only expression that remains constant is the acceleration \( a \) itself. Therefore, the answer to the question is:
- The constant expression is \( a \).

### Summary of Constant Expressions:
- The only expression that is constant is the acceleration \( a \).