Physics worksheet 2-5: Velocity-Time Graphs - Analyze position-time graphs and sketch velocity-time graphs with motion descriptions.

Let's solve problems 5 and 6 from the worksheet, where we are given position vs. time graphs, and we need to:

1. Draw the corresponding velocity vs. time graph.
2. Provide a written description of the motion.

---

🔹 Problem 5

#### 📈 Position-Time Graph:
- The graph is a straight line starting at (0,0) and ending at (4 s, 4 m).
- It has a constant positive slope.

#### ✔ Step 1: Find Velocity
Velocity is the slope of the position-time graph.

$$
\text{Slope} = \frac{\Delta x}{\Delta t} = \frac{4\,\text{m} - 0\,\text{m}}{4\,\text{s} - 0\,\text{s}} = 1\,\text{m/s}
$$

So, velocity is constant at 1 m/s for the entire 4 seconds.

#### 📊 Velocity-Time Graph:
- A horizontal line at v = 1 m/s from t = 0 to t = 4 s.
- Since it's constant, no change in velocity.

#### ✍️ Written Description:
> The object moves with a constant velocity of 1 m/s in the positive direction for 4 seconds. Its position increases linearly from 0 m to 4 m.

---

🔹 Problem 6

#### 📈 Position-Time Graph:
- From t = 0 to t = 1 s: Position goes from 0 m to 2 m → steep line.
- From t = 1 s to t = 5 s: Position goes from 2 m to 4 m → less steep line.

So, two segments with different slopes.

#### ✔ Step 1: Calculate Velocities

Segment 1 (0 to 1 s):
$$
v_1 = \frac{2\,\text{m} - 0\,\text{m}}{1\,\text{s} - 0\,\text{s}} = 2\,\text{m/s}
$$

Segment 2 (1 to 5 s):
$$
v_2 = \frac{4\,\text{m} - 2\,\text{m}}{5\,\text{s} - 1\,\text{s}} = \frac{2}{4} = 0.5\,\text{m/s}
$$

#### 📊 Velocity-Time Graph:
- From t = 0 to 1 s: horizontal line at v = 2 m/s
- From t = 1 to 5 s: horizontal line at v = 0.5 m/s

(No acceleration — both segments are straight lines, so constant velocity.)

#### ✍️ Written Description:
> The object moves with a constant velocity of 2 m/s for the first second, then slows down to a constant velocity of 0.5 m/s for the next 4 seconds. The motion is always in the positive direction, with a decrease in speed at t = 1 s.

---

⚠️ Note on Other Graphs (Blurred)

The lower two graphs appear blurred or not fully visible. However, based on the structure of the worksheet, they likely follow similar principles:

- For any position-time graph, the slope gives the velocity.
- If the slope is positive, velocity is positive.
- If the slope is negative, velocity is negative.
- If the slope is zero, velocity is zero.
- If the slope changes, velocity changes (acceleration).

But since only problems 5 and 6 are clearly visible, we’ll focus on those.

---

✔ Final Answers

#### Problem 5

- Velocity-Time Graph: Horizontal line at 1 m/s from 0 to 4 s.
- Description: Constant velocity of 1 m/s in the positive direction.

#### Problem 6

- Velocity-Time Graph:
- From 0 to 1 s: horizontal line at 2 m/s
- From 1 to 5 s: horizontal line at 0.5 m/s
- Description: Object moves at 2 m/s for first second, then at 0.5 m/s for next 4 seconds; always moving forward, but slowing down at t = 1 s.

---

Would you like me to sketch these velocity-time graphs visually (using text-based ASCII art) or help with the other two blurred problems if you can describe them?