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

Options

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

Explanation

To solve the problem, we need to analyze the motion of an object moving with constant acceleration \( a \) and determine which of the given expressions are also constant.

### Step-by-Step Solution:

1. **Understanding Constant Acceleration**:
- When an object moves with constant acceleration \( a \), it means that the acceleration does not change over time. This implies that the rate of change of velocity is uniform.

2. **Expression for Acceleration**:
- The acceleration \( a \) can be expressed mathematically as:
\[ a = \frac{dV}{dt} \]
- Since \( a \) is constant, this means that \( \frac{dV}{dt} \) is also constant.

3. **Magnitude of Acceleration**:
- The magnitude of acceleration \( |a| \) is also constant because it is given that acceleration \( a \) is constant.

4. **Velocity and Its Derivative**:
- The velocity \( V \) of the object can change over time, but since the acceleration is constant, the change in velocity \( \Delta V \) over a time interval \( \Delta t \) will be linear.
- Therefore, \( \frac{dV}{dt} \) is constant, but \( V \) itself is not constant.

5. **Other Expressions**:
- The expression \( \frac{d|V|}{dt} \) (the rate of change of the magnitude of velocity) is also constant because the acceleration is constant.
- However, expressions like \( \frac{dV^2}{dt} \) or \( \frac{dV}{|V|} \) will not be constant since they depend on the changing velocity \( V \).

6. **Conclusion**:
- The only expression that remains constant is \( \frac{dV}{dt} \) (or the acceleration) and the magnitude of acceleration \( |a| \).

### Final Answer:
The expressions that are constant are:
- \( |a| \) (magnitude of acceleration)
- \( \frac{dV}{dt} \) (acceleration)