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A point mass is moving in the x-y plane....

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 ?

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

Text Solution

AI Generated Solution

The correct Answer is:
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.
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Knowledge Check

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