Worksheet on interpreting distance-time graphs for linear motion, with questions about runners' speeds and positions.

Worksheet: Interpreting Graphs

Chapter 4: Linear Motion

#### Graph 1: Questions 1-7

We are analyzing a distance vs. time graph for three runners: Albert, Bob, and Charlie. The graph shows their positions over time, and we will use the slope of the lines to interpret their speeds and displacements.

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Question 1: What does the slope of each line on the graph tell you?

- Slope of a line on a distance vs. time graph represents speed.
- A steeper slope indicates a higher speed (the runner is moving faster).
- A shallower slope indicates a lower speed (the runner is moving slower).
- A horizontal line indicates zero speed (the runner is stationary).

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Question 2: Which runner completed the 100m race in the least amount of time? What was his time?

- From the graph, we observe that all three runners reach the 100-meter mark.
- Albert reaches the 100-meter mark first, at approximately 13 seconds.
- Bob reaches the 100-meter mark next, at approximately 15 seconds.
- Charlie reaches the 100-meter mark last, at approximately 16 seconds.

Answer: Albert completed the 100m race in the least amount of time, which is 13 seconds.

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Question 3: Which runner started out the fastest?

- To determine who started the fastest, we look at the initial slope of each line (at the beginning of the graph, near \( t = 0 \)).
- Albert has the steepest initial slope, indicating he started with the highest speed.
- Bob and Charlie have less steep initial slopes compared to Albert.

Answer: Albert started out the fastest.

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Question 4: What was Charlie doing between 8 seconds and 10.5 seconds?

- Between 8 seconds and 10.5 seconds, Charlie's line is horizontal.
- A horizontal line on a distance vs. time graph indicates that the runner is stationary (not moving).

Answer: Charlie was stationary between 8 seconds and 10.5 seconds.

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Question 5: What does a straight line on this graph tell you? A curved line?

- Straight Line:
- A straight line on a distance vs. time graph indicates constant speed.
- The slope of the line represents the speed, and since the slope is constant, the speed is constant.

- Curved Line:
- A curved line on a distance vs. time graph indicates changing speed (acceleration or deceleration).
- If the curve is upward and getting steeper, the speed is increasing.
- If the curve is upward but getting flatter, the speed is decreasing.

Answer:
- A straight line indicates constant speed.
- A curved line indicates changing speed (acceleration or deceleration).

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Question 6: At what distance and time did Albert overtake Bob?

- To find when Albert overtakes Bob, we look for the point where Albert's line crosses Bob's line.
- From the graph, Albert overtakes Bob at approximately:
- Time: 6 seconds
- Distance: 40 meters

Answer: Albert overtook Bob at a distance of 40 meters and a time of 6 seconds.

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Question 7: What was the total displacement of all three runners (\(\Delta d\))?

- Displacement is the change in position from the starting point to the ending point.
- All three runners start at 0 meters and end at 100 meters.
- Therefore, the displacement for each runner is:
\[
\Delta d = \text{Final Position} - \text{Initial Position} = 100 \, \text{meters} - 0 \, \text{meters} = 100 \, \text{meters}
\]

Answer: The total displacement of all three runners is 100 meters.

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Final Answers:

1. The slope of each line represents speed.
2. Albert completed the 100m race in 13 seconds.
3. Albert started out the fastest.
4. Charlie was stationary between 8 seconds and 10.5 seconds.
5. A straight line indicates constant speed; a curved line indicates changing speed.
6. Albert overtook Bob at a distance of 40 meters and a time of 6 seconds.
7. The total displacement of all three runners is 100 meters.

Boxed Final Answer:
\[
\boxed{13 \, \text{seconds}, \, \text{Albert}, \, \text{stationary}, \, \text{constant speed, changing speed}, \, 40 \, \text{meters}, \, 6 \, \text{seconds}, \, 100 \, \text{meters}}
\]