Speed-Distance-Time Graph Analysis Problems worksheet | Live ... - Free Printable

Let's solve both Question 4 and Question 5 step by step, using the displacement-time graphs provided.

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✔ Question 4: Ben’s Journey to Liverpool

We are given a distance-time graph showing Ben’s journey from home to Liverpool (60 km), with a stop at his friend Tim’s house.

#### Graph Details:
- X-axis: Time of day (from 13:00 to 17:00)
- Y-axis: Distance from home (in km)

The graph has three segments:
1. From 13:00 to 14:00: Distance increases from 0 to 30 km
2. From 14:00 to 15:30: Distance stays at 30 km (flat line) → stopped
3. From 15:30 to 17:00: Distance increases from 30 km to 60 km

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#### (a) Work out Ben’s speed for the first part of his journey.

Speed = Distance ÷ Time

- Distance covered: 30 km (from 0 to 30 km)
- Time taken: 14:00 – 13:00 = 1 hour

$$
\text{Speed} = \frac{30\,\text{km}}{1\,\text{hour}} = 30\,\text{km/h}
$$

✔ Answer: 30 km/h

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#### (b) How long did Ben spend visiting Tim?

He is stationary (distance not changing) from 14:00 to 15:30.

- Duration = 15:30 – 14:00 = 1 hour 30 minutes

✔ Answer: 1 hour 30 minutes (or 1.5 hours)

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#### (c) Work out Ben’s speed for the last part of his journey.

- Distance covered: 60 km – 30 km = 30 km
- Time taken: 17:00 – 15:30 = 1 hour 30 minutes = 1.5 hours

$$
\text{Speed} = \frac{30\,\text{km}}{1.5\,\text{hours}} = 20\,\text{km/h}
$$

✔ Answer: 20 km/h

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✔ Question 5: Laura’s Cycle to Post Office

Graph shows distance from home over time.

#### Graph Details:
- X-axis: Time from 11:00 to 12:00
- Y-axis: Distance from home in km (up to 4 km)

Three segments:
1. 11:00 → 11:20: Rising to 4 km → going to post office
2. 11:20 → 11:40: Flat at 4 km → stopped at post office
3. 11:40 → 12:00: Falling back to 0 km → returning home

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#### (a) How long did it take Laura to cycle to the post office?

She starts at 11:00 and reaches 4 km at 11:20

- Time taken = 11:20 – 11:00 = 20 minutes

✔ Answer: 20 minutes

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#### (b) Work out Laura’s speed cycling to the post office.

- Distance = 4 km
- Time = 20 minutes = $ \frac{20}{60} = \frac{1}{3} $ hours

$$
\text{Speed} = \frac{4\,\text{km}}{\frac{1}{3}\,\text{h}} = 4 \times 3 = 12\,\text{km/h}
$$

✔ Answer: 12 km/h

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#### (c) How long did Laura spend at the post office?

She arrives at 11:20 and leaves at 11:40.

- Duration = 11:40 – 11:20 = 20 minutes

✔ Answer: 20 minutes

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#### (d) Work out Laura’s speed cycling back home.

- Distance = 4 km (back from post office)
- Time = 12:00 – 11:40 = 20 minutes = $ \frac{1}{3} $ hours

$$
\text{Speed} = \frac{4\,\text{km}}{\frac{1}{3}\,\text{h}} = 12\,\text{km/h}
$$

✔ Answer: 12 km/h

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✔ Final Answers Summary:

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Question 4: Ben

(a) Speed (first part): 30 km/h
(b) Time visiting Tim: 1 hour 30 minutes
(c) Speed (last part): 20 km/h

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Question 5: Laura

(a) Time to post office: 20 minutes
(b) Speed to post office: 12 km/h
(c) Time at post office: 20 minutes
(d) Speed returning home: 12 km/h

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🔍 Explanation Recap:

- In distance-time graphs, slope = speed.
- Steeper slope = higher speed
- Horizontal line = stopped (speed = 0)
- Time intervals are read directly from the x-axis.
- Always convert time to hours when calculating speed in km/h.

Let me know if you'd like this explained visually or with diagrams!