50 Distance Vs Time Graph Worksheet - Free Printable

It looks like you've uploaded a worksheet titled "Drawing Distance-Time Graphs" from Cazoom Maths, and it includes several problems involving distance-time graphs. The page shows both the questions and their answers already drawn in red. However, since you're asking to solve the problem and explain the solution, I'll go through each question step by step, explaining how to draw the correct distance-time graph and why it looks the way it does.

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🔹 Question 1: Draw a line that represents the speeds given

We are given three scenarios with different speeds and need to draw straight-line graphs (since speed is constant) on distance-time graphs.

#### ✔ Graph 1: 100 km/h
- Speed: 100 km/h
- Axes: Distance (km), Time (hours)
- At t = 1 hour → d = 100 km
- At t = 2 hours → d = 200 km

✔ So, the graph is a straight line starting at (0,0) and going through (1,100), (2,200), etc.
- This is correctly shown as a steep red line.

> ✔️ Explanation: Constant speed means a straight line. Steeper slope = faster speed.

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#### ✔ Graph 2: 2 m/s
- Speed: 2 meters per second
- Axes: Distance (m), Time (seconds)
- At t = 5 s → d = 10 m
- At t = 10 s → d = 20 m
- At t = 20 s → d = 40 m

✔ The line goes from (0,0) to (20,40). Slope = 40/20 = 2 m/s → correct.

> ✔️ Explanation: Speed = gradient of the line. Gradient = rise/run = distance/time.

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#### ✔ Graph 3: 15 mph
- Speed: 15 miles per hour
- Axes: Distance (miles), Time (hours)
- At t = 1 hour → d = 15 miles
- At t = 2 hours → d = 30 miles

✔ The line goes from (0,0) to (2,30). So, slope = 30/2 = 15 mph → correct.

> ✔️ Explanation: Even though the time axis is in hours, we can still plot directly using the speed.

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🔹 Question 2: Car travels 30 miles in 30 minutes, stops for 10 minutes, then continues at 45 mph for 20 minutes

Let’s break this down:

#### Step 1: First leg – 30 miles in 30 minutes
- Time: 0 to 30 min
- Distance: 0 to 30 miles
- Speed = 30 miles / 0.5 hours = 60 mph → but we don’t need speed for graphing
- Plot a straight line from (0,0) to (30,30)

#### Step 2: Stop at service station – 10 minutes
- Time: 30 to 40 min
- Distance stays at 30 miles
- Horizontal line at 30 miles

#### Step 3: Continue at 45 mph for 20 minutes
- Time: 40 to 60 min
- Speed = 45 mph = 45 miles per hour
- In 20 minutes (1/3 hour): distance = 45 × (1/3) = 15 miles
- So new distance = 30 + 15 = 45 miles
- Plot line from (40,30) to (60,45)

✔ The graph shows:
- Line from (0,0) to (30,30)
- Flat line from (30,30) to (40,30)
- Then rising line to (60,45)

> ✔️ Explanation: When stopped, distance doesn't change → horizontal line. When moving again, slope reflects new speed.

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🔹 Question 3: Girl walks at 1.5 m/s for 20 seconds, stops for 15 seconds, walks back at 2 m/s

#### Step 1: Walk forward at 1.5 m/s for 20 sec
- Distance = 1.5 × 20 = 30 meters
- From t = 0 to 20 s: line from (0,0) to (20,30)

#### Step 2: Stop for 15 seconds
- From t = 20 to 35 s: distance stays at 30 m → horizontal line

#### Step 3: Walk back to start at 2 m/s
- Distance to cover: 30 meters
- Time = distance / speed = 30 / 2 = 15 seconds
- So from t = 35 to 50 s: distance decreases from 30 to 0
- Line from (35,30) to (50,0)

✔ The graph shows:
- Upward line to (20,30)
- Flat line to (35,30)
- Downward line to (50,0)

> ✔️ Explanation: Returning to start means distance decreases → negative slope. But note: in distance-time graphs, distance is usually taken as displacement from origin, so returning reduces distance.

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🔹 Question 4: Car drives 1.5 hours at 60 mph, stops for 30 min, returns at 45 mph

#### Step 1: Drive 1.5 hours at 60 mph
- Distance = 60 × 1.5 = 90 miles
- From t = 0 to 1.5 h: line from (0,0) to (1.5,90)

#### Step 2: Stop for 30 minutes (0.5 hours)
- From t = 1.5 to 2.0 h: distance remains 90 miles → flat line

#### Step 3: Return at 45 mph
- Distance to cover: 90 miles
- Time = 90 / 45 = 2 hours
- So from t = 2.0 to 4.0 h: distance drops from 90 to 0
- Line from (2,90) to (4,0)

✔ The graph shows:
- Rising line to (1.5,90)
- Flat line to (2,90)
- Falling line to (4,0)

> ✔️ Explanation: The return journey takes longer (2 hours vs. 1.5 hours) because slower speed → shallower slope downward.

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✔ Summary of Key Concepts:

| Feature | Meaning |
|--------|--------|
| Straight line | Constant speed |
| Steeper slope | Higher speed |
| Flat line | Stationary (stopped) |
| Downward slope | Moving back toward start |
| Gradient (slope) | Speed = distance/time |

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🟩 Final Notes:

The answers provided in red on your worksheet are correct for all four questions. They visually represent:
- Constant speed with straight lines
- Stops with horizontal segments
- Return trips with decreasing distance (downward slopes)

If you were asked to draw these graphs yourself, follow the steps above to ensure accuracy in scaling and labeling.

Would you like me to generate a printable version or help you recreate one of these graphs?