This worksheet, titled 'Speed Time Graphs 4', challenges students to draw distance-time graphs based on specific speeds and travel scenarios.

Let's go through each of the four problems in the worksheet "Speed Time Graphs 4" and solve them step by step with explanations.

---

1) Draw a line that represents the speeds given.

We are given three different speed values, and we need to draw a distance-time graph for each (i.e., a straight line showing constant speed). The slope of the line will represent the speed.

#### a) 100 km/h
- Graph: Distance (km) vs Time (hours)
- Speed = 100 km/h → So every hour, distance increases by 100 km
- Plot points:
- At 0 hours → 0 km
- At 1 hour → 100 km
- At 2 hours → 200 km
- Draw a straight line from (0,0) to (2,200)

✔ Result: A straight diagonal line rising steeply.

#### b) 2 m/s
- Graph: Distance (m) vs Time (seconds)
- Speed = 2 m/s → Every second, distance increases by 2 meters
- Points:
- (0,0), (5,10), (10,20), (15,30), (20,40)
- Draw a straight line from (0,0) to (20,40)

✔ Result: A moderately steep line.

#### c) 15 mph
- Graph: Distance (miles) vs Time (hours)
- Speed = 15 miles per hour
- Points:
- (0,0), (1,15), (2,30)
- Draw a straight line from (0,0) to (2,30)

✔ Result: A gentle slope.

> 💡 Note: All three graphs are straight lines, since speed is constant. The steeper the line, the faster the speed.

---

2) Car journey: 30 miles in 30 min → Stop 10 min → 45 mph for 20 min

We need to draw a distance-time graph.

#### Step-by-step:

- First leg: Travels 30 miles in 30 minutes at constant speed.
- Speed = 30 miles / 0.5 hours = 60 mph
- From t = 0 to t = 30 min (0.5 h): distance increases from 0 to 30 miles

- Second leg: Stops at service station for 10 minutes
- From t = 30 to 40 min: distance stays at 30 miles → horizontal line

- Third leg: Travels 20 minutes at 45 mph
- Distance covered = 45 mph × (1/3) h = 15 miles
- So from t = 40 to 60 min: distance increases from 30 to 45 miles

#### Graph Features:
- Line from (0,0) to (30,30)
- Horizontal line from (30,30) to (40,30)
- Line from (40,30) to (60,45)

✔ Result: Three segments: upward, flat, upward again.

---

3) Girl walks: 1.5 m/s for 20 s → stops 15 s → returns at 2 m/s

Draw distance-time graph.

#### Step-by-step:

- First leg: Walks at 1.5 m/s for 20 seconds
- Distance = 1.5 × 20 = 30 meters
- From t = 0 to 20 s: distance goes from 0 to 30 m

- Second leg: Stops for 15 seconds
- From t = 20 to 35 s: distance remains at 30 m → horizontal line

- Third leg: Walks back to start at 2 m/s
- Distance to cover = 30 m
- Time = 30 / 2 = 15 seconds
- So from t = 35 to 50 s: distance decreases from 30 to 0 m

#### Graph Features:
- Line from (0,0) to (20,30)
- Horizontal line from (20,30) to (35,30)
- Line from (35,30) to (50,0)

✔ Result: Upward, flat, then downward (back to origin).

> 🚩 Important: When returning, the graph slopes downward, but time still moves forward.

---

4) Car drives: 1.5 hours at 60 mph → stops 30 min → returns at 45 mph

Draw distance-time graph.

#### Step-by-step:

- First leg: Drives 1.5 hours at 60 mph
- Distance = 60 × 1.5 = 90 miles
- From t = 0 to 1.5 h: distance increases from 0 to 90 miles

- Second leg: Stops for 30 minutes (0.5 hours)
- From t = 1.5 to 2.0 h: distance stays at 90 miles → horizontal line

- Third leg: Returns at 45 mph
- Distance to cover = 90 miles
- Time = 90 / 45 = 2 hours
- So from t = 2.0 to 4.0 h: distance decreases from 90 to 0 miles

#### Graph Features:
- Line from (0,0) to (1.5,90)
- Horizontal line from (1.5,90) to (2.0,90)
- Line from (2.0,90) to (4.0,0)

✔ Result: Upward, flat, then downward to origin.

> 📌 Note: The return trip takes longer (2 hours) than the outward trip (1.5 hours), so the downward slope is less steep.

---

✔ Summary of Graph Characteristics

| Segment | Description | Graph Shape |
|--------|-------------|-------------|
| Constant speed | Straight line with positive slope | Rising |
| Stopped | No movement | Horizontal line |
| Returning | Moving back toward start | Falling line (negative slope) |

---

Final Tips for Drawing These Graphs:

1. Label axes clearly (Time and Distance).
2. Use consistent scales.
3. Plot key points and connect them appropriately.
4. Remember: Distance-time graphs show position over time, not speed directly — but the slope gives speed.

---

If you'd like, I can provide visual descriptions or help you sketch these on paper. Let me know!