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This question asks for a representation of two balls rolling down an incline, one being released one second after the first. Let's break it down:

**(a) Represent the motion:**
1. **Motion Diagrams:**
   - The first ball starts moving at \( t = 0 \).
   - The second ball starts moving at \( t = 1 \, \text{second} \).
   - Both balls experience constant acceleration due to gravity, which would result in increasing distances between dots on their respective motion diagrams. Since both are subject to the same forces, their motion diagrams will be similar, but the second ball's diagram will be shifted by 1 second.

2. **Position-Time Graphs:**
   - For both balls, the position-time graph is parabolic, representing constant acceleration.
   - The first ball's graph will start at \( t = 0 \), while the second ball's graph starts at \( t = 1 \, \text{second} \). 
   - The second ball’s position-time graph will follow the same curve but shifted rightwards by 1 second.

3. **Velocity-Time Graphs:**
   - The velocity of each ball increases linearly over time because they are accelerating.
   - The first ball’s velocity increases starting at \( t = 0 \).
   - The second ball’s velocity graph starts at \( t = 1 \, \text{second} \), following the same slope as the first ball’s graph, but with a 1-second delay.

**(b) Distance between the balls:**
   - Initially, when the second ball starts moving, the first ball is already rolling and has gained velocity.
   - As both balls are accelerating at the same rate, the distance between them will initially increase.
   - However, after some time, the second ball will catch up because both have the same acceleration and the difference in their velocities decreases as time progresses.

Would you like a more detailed explanation or graphical representation?

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Here are five related questions to deepen your understanding:
1. How does the acceleration of the balls affect their velocity over time?
2. What would happen if the incline had friction?
3. How would the motion change if one of the balls had a different mass?
4. Can you explain how the distance between the two balls evolves over a longer time?
5. What if the second ball were released 2 seconds later instead of 1 second?

**Tip:** In motion problems involving inclines, it's often helpful to break forces into components parallel and perpendicular to the surface for easier analysis.

A ball is rolled down an incline. One second later a second ball is released down the same incline. (a) Represent the motion of these two balls with motion diagrams, position-time graphs, and velocity-time graphs. (b) Use your representations to explain what happens to the distance between the two balls as they roll down the incline.

Analyze the motion of two balls rolling down an incline with a one-second delay. Understand the motion diagrams, position-time graphs, and velocity-time graphs for constant acceleration. Suitable for high school students studying kinematics.

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