Worksheet on interpreting distance-time graphs for motion analysis.
A worksheet with two questions analyzing distance-time graphs, showing a journey to the zoo and a trip to a grandmother's house, including graph analysis and comprehension questions.
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Show Answer Key & Explanations
Step-by-step solution for: Speed-Distance-Time Graph Analysis Problems worksheet | Live ...
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Show Answer Key & Explanations
Step-by-step solution for: Speed-Distance-Time Graph Analysis Problems worksheet | Live ...
Let's solve both questions step by step using the distance-time graphs provided.
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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:
---
(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
---
(b) What time did they stop for a picnic?
- A flat horizontal line on a distance-time graph means no movement (stopped).
- The flat line appears from 10:00 to 10:30.
- So, they stopped for a picnic starting at 10:00.
✔ Answer: 10:00
---
(c) How far had they travelled when they stopped for a picnic?
- At 10:00, the distance is 50 miles (read from the y-axis).
- This is the distance from school when they stopped.
✔ Answer: 50 miles
---
(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
---
(e) What time did they arrive at the zoo?
- The graph ends at 11:30, where the distance reaches its maximum (90 miles).
- So, they arrived at the zoo at 11:30.
✔ Answer: 11:30
---
(f) How far is the zoo from school?
- The final distance on the graph is 90 miles.
✔ Answer: 90 miles
---
| Part | Answer |
|------|--------|
| (a) | 09:00 |
| (b) | 10:00 |
| (c) | 50 miles |
| (d) | 30 minutes |
| (e) | 11:30 |
| (f) | 90 miles |
---
Given: Distance-time graph of 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)
Let’s go through each part.
---
(a) What time did Emma begin her journey?
- The graph starts rising at 7:30 AM (since it's zero until then).
- So, she began at 7:30 AM.
✔ Answer: 7:30 AM
---
(b) How far was Emma from home at 8am?
- At 8:00 AM, look at the graph: the distance is about 30 miles.
- (From 7:30 to 8:00, the graph goes up steadily to 30 miles.)
✔ Answer: 30 miles
---
(c) How long did Emma stay at her grandmother’s house?
- The flat horizontal line at 40 miles 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
---
(d) What time did Emma leave her grandmother’s house?
- She leaves when the graph starts decreasing from 40 miles.
- That happens at 10:00 AM.
✔ Answer: 10:00 AM
---
(e) How far was Emma from home at 11:45?
- From 10:00 to 12:00, she is returning home.
- At 11:45, she is still on the way back.
- Between 11:00 and 12:00, the graph drops from 30 miles to 0.
- So, in 60 minutes, she travels 30 miles → speed = 30 mph.
- From 11:00 to 11:45 is 45 minutes = 0.75 hours.
- Distance covered in that time: $ 30 \times 0.75 = 22.5 $ miles.
- So, at 11:45, she is $ 30 - 22.5 = 7.5 $ miles from home.
But wait — let's check the graph more carefully.
Looking at the graph:
- At 11:00, distance = 30 miles
- At 12:00, distance = 0 miles
- So, linear decrease from 30 miles at 11:00 to 0 at 12:00
So, in 60 minutes, she covers 30 miles → 0.5 miles per minute.
From 11:00 to 11:45 = 45 minutes → distance covered = $ 45 \times 0.5 = 22.5 $ miles
So, remaining distance from home = $ 30 - 22.5 = 7.5 $ miles
✔ Answer: 7.5 miles
---
(f) How far did Emma travel in total?
- To grandmother’s house: 40 miles
- Back home: 40 miles
- Total distance = $ 40 + 40 = 80 $ miles
✔ Answer: 80 miles
---
| 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 |
---
- In a distance-time graph:
- Slope = speed (steeper = faster)
- Flat line = stopped (no movement)
- Increasing slope = moving away
- Decreasing slope = returning
- Total distance traveled = sum of all distances moved (not displacement).
Let me know if you'd like these answers formatted as a printable worksheet or need help interpreting similar graphs!
---
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:
---
(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
---
(b) What time did they stop for a picnic?
- A flat horizontal line on a distance-time graph means no movement (stopped).
- The flat line appears from 10:00 to 10:30.
- So, they stopped for a picnic starting at 10:00.
✔ Answer: 10:00
---
(c) How far had they travelled when they stopped for a picnic?
- At 10:00, the distance is 50 miles (read from the y-axis).
- This is the distance from school when they stopped.
✔ Answer: 50 miles
---
(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
---
(e) What time did they arrive at the zoo?
- The graph ends at 11:30, where the distance reaches its maximum (90 miles).
- So, they arrived at the zoo at 11:30.
✔ Answer: 11:30
---
(f) How far is the zoo from school?
- The final distance on the graph is 90 miles.
✔ Answer: 90 miles
---
✔ Summary for Question 1:
| Part | Answer |
|------|--------|
| (a) | 09:00 |
| (b) | 10:00 |
| (c) | 50 miles |
| (d) | 30 minutes |
| (e) | 11:30 |
| (f) | 90 miles |
---
Question 2: Emma’s Journey to Grandmother’s House
Given: Distance-time graph of 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)
Let’s go through each part.
---
(a) What time did Emma begin her journey?
- The graph starts rising at 7:30 AM (since it's zero until then).
- So, she began at 7:30 AM.
✔ Answer: 7:30 AM
---
(b) How far was Emma from home at 8am?
- At 8:00 AM, look at the graph: the distance is about 30 miles.
- (From 7:30 to 8:00, the graph goes up steadily to 30 miles.)
✔ Answer: 30 miles
---
(c) How long did Emma stay at her grandmother’s house?
- The flat horizontal line at 40 miles 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
---
(d) What time did Emma leave her grandmother’s house?
- She leaves when the graph starts decreasing from 40 miles.
- That happens at 10:00 AM.
✔ Answer: 10:00 AM
---
(e) How far was Emma from home at 11:45?
- From 10:00 to 12:00, she is returning home.
- At 11:45, she is still on the way back.
- Between 11:00 and 12:00, the graph drops from 30 miles to 0.
- So, in 60 minutes, she travels 30 miles → speed = 30 mph.
- From 11:00 to 11:45 is 45 minutes = 0.75 hours.
- Distance covered in that time: $ 30 \times 0.75 = 22.5 $ miles.
- So, at 11:45, she is $ 30 - 22.5 = 7.5 $ miles from home.
But wait — let's check the graph more carefully.
Looking at the graph:
- At 11:00, distance = 30 miles
- At 12:00, distance = 0 miles
- So, linear decrease from 30 miles at 11:00 to 0 at 12:00
So, in 60 minutes, she covers 30 miles → 0.5 miles per minute.
From 11:00 to 11:45 = 45 minutes → distance covered = $ 45 \times 0.5 = 22.5 $ miles
So, remaining distance from home = $ 30 - 22.5 = 7.5 $ miles
✔ Answer: 7.5 miles
---
(f) How far did Emma travel in total?
- To grandmother’s house: 40 miles
- Back home: 40 miles
- Total distance = $ 40 + 40 = 80 $ miles
✔ Answer: 80 miles
---
✔ 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 |
---
📌 Key Concepts Used:
- In a distance-time graph:
- Slope = speed (steeper = faster)
- Flat line = stopped (no movement)
- Increasing slope = moving away
- Decreasing slope = returning
- Total distance traveled = sum of all distances moved (not displacement).
Let me know if you'd like these answers formatted as a printable worksheet or need help interpreting similar graphs!
Parent Tip: Review the logic above to help your child master the concept of time graph worksheet.
![Distance Time Graph Worksheet - GCSE Maths [FREE] - Third Space ...](/images2/time-graph-worksheet/time-graph-worksheet-34.jpg)
