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

Let's solve both questions step by step using the distance-time graphs provided.

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Question 1: Class 8A’s Journey to the Zoo

We are given a distance-time graph showing the journey of class 8A from school to the zoo, with a picnic stop along the way.

#### Graph Details:
- Y-axis: Distance from school (in miles)
- X-axis: Time of day (from 09:00 to 11:30)

Let’s analyze each part:

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(a) What time did the bus leave school?

- The graph starts at 09:00, and the distance begins increasing from 0.
- So, the bus left school at 09:00.

✔ Answer: 09:00

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(b) What time did they stop for a picnic?

- A flat horizontal line on a distance-time graph means no movement (stopped).
- The first flat section starts at 10:00 and ends at 10:30.
- So, they stopped at 10:00.

✔ Answer: 10:00

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(c) How far had they travelled when they stopped for a picnic?

- At 10:00, the distance from school is 50 miles.
- This is where the flat line starts.

✔ Answer: 50 miles

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(d) How long did they stop for?

- They stopped from 10:00 to 10:30.
- Duration = 10:30 – 10:00 = 30 minutes

✔ Answer: 30 minutes

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(e) What time did they arrive at the zoo?

- The journey ends when the graph stops increasing — at 11:30.
- The final point shows arrival at the zoo.

✔ Answer: 11:30

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(f) How far is the zoo from school?

- Final distance on the graph at 11:30 is 90 miles.

✔ Answer: 90 miles

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✔ Summary for Question 1:

| Part | Answer |
|------|--------|
| (a) | 09:00 |
| (b) | 10:00 |
| (c) | 50 miles |
| (d) | 30 minutes |
| (e) | 11:30 |
| (f) | 90 miles |

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Question 2: Emma’s Journey to Her Grandmother’s House

We have another distance-time graph showing Emma's trip to her grandmother’s house and back.

#### Graph Details:
- Y-axis: Distance from home (in miles)
- X-axis: Time from 7:00 AM to 12:00 PM

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(a) What time did Emma begin her journey?

- The graph starts rising at 7:30 AM (since it's zero until then).
- So she started at 7:30 AM.

✔ Answer: 7:30 AM

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(b) How far was Emma from home at 8am?

- At 8:00 AM, find the y-value.
- From the graph, at 8:00, distance ≈ 30 miles.

✔ Answer: 30 miles

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(c) How long did Emma stay at her grandmother’s house?

- The flat horizontal part represents staying at the house.
- It starts at 8:30 AM and ends at 10:00 AM.
- Duration = 10:00 – 8:30 = 1 hour 30 minutes

✔ Answer: 1 hour 30 minutes

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(d) What time did Emma leave her grandmother’s house?

- She leaves when the graph starts decreasing again.
- That happens at 10:00 AM.

✔ Answer: 10:00 AM

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(e) How far was Emma from home at 11:45?

- At 11:45, look at the graph.
- Between 11:00 and 12:00, the graph is descending from 30 miles to 0.
- At 11:00: 30 miles
- At 12:00: 0 miles
- So in 60 minutes, she travels 30 miles → speed = 30 mph
- From 11:00 to 11:45 = 45 minutes = 0.75 hours
- Distance covered in 45 min = 30 × 0.75 = 22.5 miles
- So distance from home = 30 – 22.5 = 7.5 miles

✔ Answer: 7.5 miles

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(f) How far did Emma travel in total?

- To grandmother’s house: 40 miles (maximum distance)
- Return journey: also 40 miles
- Total = 40 + 40 = 80 miles

✔ Answer: 80 miles

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✔ Summary for Question 2:

| Part | Answer |
|------|--------|
| (a) | 7:30 AM |
| (b) | 30 miles |
| (c) | 1 hour 30 minutes |
| (d) | 10:00 AM |
| (e) | 7.5 miles |
| (f) | 80 miles |

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📌 Key Concepts Used:

- Distance-time graphs:
- Slope = speed (steeper = faster)
- Flat line = stopped (no movement)
- Increasing line = moving away
- Decreasing line = returning
- Total distance = sum of all distances traveled (not displacement)

Let me know if you'd like these explained visually or need help interpreting similar graphs!