Part I: Fill in the Table

Let's fill in the table based on the concepts of motion graphs.

1. Position vs. Time Graph

• Positive Slope:

  • Shape: A straight line slanting upwards from left to right.
  • Motion Interpretation: The object is moving forward with constant velocity.

• Negative Slope:

  • Shape: A straight line slanting downwards from left to right.
  • Motion Interpretation: The object is moving backward (or in the opposite direction) with constant velocity.

• Zero Slope:

  • Shape: A horizontal straight line.
  • Motion Interpretation: The object is at rest (no change in position).

2. Velocity vs. Time Graph

• Positive Slope:

  • Shape: A straight line slanting upwards from left to right.
  • Motion Interpretation: The object is accelerating (increasing velocity).

• Negative Slope:

  • Shape: A straight line slanting downwards from left to right.
  • Motion Interpretation: The object is decelerating (decreasing velocity).

• Zero Slope:

  • Shape: A horizontal straight line.
  • Motion Interpretation: The object is moving with constant velocity (no change in velocity).

Part II: Problem-Solving

Let's solve the given problems one by one.

1. Sara's Acceleration Problem

Sara starts from rest (initial velocity $u = 0$) and accelerates at a rate of $a = 2 \, \text{m/s}^2$ for $t = 10 \, \text{seconds}$.

• Final Velocity $v$: $v = u + at = 0 + (2 \times 10) = 20 \, \text{m/s}$

• Distance Traveled $s$: $s = ut + \frac{1}{2}at^2 = 0 \times 10 + \frac{1}{2} \times 2 \times 10^2 = \frac{1}{2} \times 2 \times 100 = 100 \, \text{meters}$

Sara travels 100 meters.

2. Alice's Constant Velocity Problem

Alice maintains a constant velocity of $v = 15 \, \text{m/s}$ for $t = 20 \, \text{seconds}$.

• Distance Traveled $s$: $s = vt = 15 \times 20 = 300 \, \text{meters}$

Alice travels 300 meters.

3. Emily's Displacement Problem

Emily stands still for 5 minutes (which is $t = 5 \times 60 = 300 \, \text{seconds}$).

• Displacement: Since she is standing still, her displacement is $0 \, \text{meters}$.

Do you need further details or have any questions? Here are some related questions to expand on this:

1. How would the position vs. time graph look for an object that starts at a non-zero position and moves with constant velocity?
2. What happens to the velocity vs. time graph if an object accelerates uniformly, then suddenly stops?
3. How can the area under a velocity vs. time graph help determine the distance traveled?
4. What type of motion would be represented by a position vs. time graph that curves upwards?
5. How does a negative slope in a velocity vs. time graph relate to real-life situations?

Tip: Always pay attention to the initial conditions given in a problem (like starting from rest) as they are crucial in determining how you approach the calculations.