A point mass is moving in the x-y plane. Its acceleration is a constant vector perpendicular to the x-axis. Which of the following do/does not charge with time ?

Options

A. only y-component of its velocity vector
B. only x-component of its velocity vector
C. only y-component of its acceleration vector
D. only x-component of its acceleration vector

Answer

To solve the problem, we need to analyze the motion of a point mass in the x-y plane with a constant acceleration vector that is perpendicular to the x-axis.

### Step-by-Step Solution:

1. **Understanding the Acceleration**:
- The acceleration vector is constant and perpendicular to the x-axis. This means it can only have a component in the y-direction. Therefore, we can denote the acceleration as \( \vec{a} = (0, a_y) \), where \( a_y \) is a constant.

2. **Analyzing the x-component of Velocity**:
- Since there is no acceleration in the x-direction (i.e., \( a_x = 0 \)), the velocity in the x-direction, \( v_x \), will remain constant. This means that \( v_x(t) = v_{x0} \), where \( v_{x0} \) is the initial velocity in the x-direction.

3. **Analyzing the y-component of Velocity**:
- The y-component of velocity, \( v_y \), will change with time due to the constant acceleration in the y-direction. The relationship is given by:
\[ v_y(t) = v_{y0} + a_y t \]
- Here, \( v_{y0} \) is the initial velocity in the y-direction. Thus, \( v_y \) is not constant and will change with time.

4. **Analyzing the Components of Acceleration**:
- The acceleration in the y-direction is constant (as given in the problem), so \( a_y \) does not change with time.
- The x-component of acceleration is zero, which is also constant. Therefore, \( a_x = 0 \) does not change with time.

5. **Conclusion**:
- From the analysis:
- The x-component of velocity remains constant.
- The y-component of velocity changes with time.
- The y-component of acceleration remains constant.
- The x-component of acceleration remains constant (and is zero).
- Therefore, the quantities that do not change with time are:
- The x-component of velocity.
- The y-component of acceleration.
- The x-component of acceleration.

### Final Answer:
The quantities that do not change with time are:
- The x-component of velocity.
- The y-component of acceleration.
- The x-component of acceleration.