Measures, Units & Real-life Graphs - Free Printable

To solve the problem, we need to analyze the distance-time graph and evaluate each statement based on the information provided. Let's go through each statement step by step.

Graph Analysis

- The graph shows Emma's journey over time, with distance from home on the y-axis and time in minutes on the x-axis.
- There are five stages labeled as 1, 2, 3, 4, and 5.

Statements Evaluation

#### A. During stage 1, Emma travelled at 3 km/minute.
- Stage 1 is the initial segment from \( t = 0 \) to \( t = 10 \) minutes.
- At \( t = 0 \), the distance is 0 km.
- At \( t = 10 \) minutes, the distance is 5 km.
- Speed during stage 1:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{5 \text{ km}}{10 \text{ minutes}} = 0.5 \text{ km/minute}
\]
- The statement claims a speed of 3 km/minute, which is incorrect.

Conclusion: False

#### B. Emma was stationary during stage 2.
- Stage 2 is the horizontal segment from \( t = 10 \) to \( t = 25 \) minutes.
- A horizontal line on a distance-time graph indicates that the distance from home is constant, meaning Emma was stationary.

Conclusion: True

#### C. The graph shows that Emma reached the top of two hills.
- The graph shows two peaks:
- One at \( t = 10 \) minutes (5 km).
- Another at \( t = 60 \) minutes (7 km).
- These peaks can be interpreted as "tops of hills" in the context of the graph.

Conclusion: True

#### D. Emma travelled 4000m during Stage 4.
- Stage 4 is the segment from \( t = 40 \) to \( t = 55 \) minutes.
- At \( t = 40 \) minutes, the distance is 3 km.
- At \( t = 55 \) minutes, the distance is 5 km.
- Distance travelled during stage 4:
\[
\text{Distance} = 5 \text{ km} - 3 \text{ km} = 2 \text{ km} = 2000 \text{ m}
\]
- The statement claims 4000 m, which is incorrect.

Conclusion: False

#### E. The slowest part of Emma's journey was during stage 3.
- Stage 3 is the segment from \( t = 25 \) to \( t = 40 \) minutes.
- At \( t = 25 \) minutes, the distance is 5 km.
- At \( t = 40 \) minutes, the distance is 3 km.
- Speed during stage 3:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{5 \text{ km} - 3 \text{ km}}{40 \text{ minutes} - 25 \text{ minutes}} = \frac{2 \text{ km}}{15 \text{ minutes}} = \frac{2}{15} \text{ km/minute}
\]
- Comparing speeds:
- Stage 1: \( 0.5 \text{ km/minute} \)
- Stage 2: \( 0 \text{ km/minute} \) (stationary)
- Stage 3: \( \frac{2}{15} \text{ km/minute} \approx 0.133 \text{ km/minute} \)
- Stage 4: \( \frac{2 \text{ km}}{15 \text{ minutes}} = \frac{2}{15} \text{ km/minute} \approx 0.133 \text{ km/minute} \)
- Stage 5: \( \frac{2 \text{ km}}{15 \text{ minutes}} = \frac{2}{15} \text{ km/minute} \approx 0.133 \text{ km/minute} \)
- Stage 3 has the same speed as stages 4 and 5, but it is not the slowest since stage 2 is stationary (0 km/minute).

Conclusion: False

#### F. Emma's average speed over the whole journey was 7 km/h.
- Total distance travelled:
\[
\text{Final distance} - \text{Initial distance} = 7 \text{ km} - 0 \text{ km} = 7 \text{ km}
\]
- Total time taken:
\[
60 \text{ minutes} = 1 \text{ hour}
\]
- Average speed:
\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{7 \text{ km}}{1 \text{ hour}} = 7 \text{ km/h}
\]

Conclusion: True

#### G. Emma was travelling faster during stage 4 than stage 1.
- Stage 1 speed: \( 0.5 \text{ km/minute} \)
- Stage 4 speed: \( \frac{2 \text{ km}}{15 \text{ minutes}} = \frac{2}{15} \text{ km/minute} \approx 0.133 \text{ km/minute} \)
- Comparing the speeds:
\[
0.5 \text{ km/minute} > 0.133 \text{ km/minute}
\]
- Emma was actually slower during stage 4 than stage 1.

Conclusion: False

#### H. When she was 5 minutes into her journey, Emma had travelled 3 km.
- At \( t = 5 \) minutes, the distance from the graph is approximately 2.5 km, not 3 km.

Conclusion: False

True Statements

- B. Emma was stationary during stage 2.
- C. The graph shows that Emma reached the top of two hills.
- F. Emma's average speed over the whole journey was 7 km/h.

Final Answer

\[
\boxed{B, C, F}
\]