2.6 Distance Time Graphs Worksheet #2 | Study notes Physics | Docsity - Free Printable

Let's solve the worksheet step by step.

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Question 1: Describe the motion shown in each distance-time graph. Write a few sentences describing a situation that could be represented by each graph.

We analyze each graph based on how distance changes with time:

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#### a)
- The graph shows a straight line with a constant positive slope.
- This means the object is moving at a constant speed away from the starting point.
- Situation: A person walks steadily away from their house at a constant pace, such as walking to school at a steady speed.

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#### b)
- The graph shows a curve that starts flat and becomes steeper over time.
- This indicates increasing speed (acceleration) — the object is covering more distance in less time as time progresses.
- Situation: A car starting from rest and speeding up on a highway, like accelerating from a stoplight.

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#### c)
- The graph is a horizontal line, meaning distance does not change over time.
- The object is not moving — it is at rest.
- Situation: A student sitting at their desk during class, not moving from their seat.

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#### d)
- The graph shows a straight line with a negative slope.
- Distance decreases at a constant rate → the object is moving toward the starting point at a constant speed.
- Situation: A person walking back home from a park at a steady pace.

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#### e)
- The graph starts with a gentle curve, then flattens out.
- This suggests the object moves slowly at first, then speeds up, and finally slows down or stops.
- Situation: A cyclist starts riding slowly, then increases speed, and eventually levels off as they maintain a steady pace or approach a destination.

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#### f)
- The graph is a parabola-like shape: distance increases, reaches a maximum, then decreases back to zero.
- The object moves away from the start, reaches a farthest point, then returns to the starting point.
- Situation: A ball thrown upward into the air — it goes up, stops briefly at the peak, then falls back down to the ground.

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Question 2: Which of the graphs in question 1 show linear relations between distance and time? Justify your answer.

A linear relation means the graph is a straight line, indicating a constant rate of change (i.e., constant speed).

Let’s examine each:

- a) ✔ Straight line → Linear
- b) ✘ Curved → Non-linear
- c) ✔ Horizontal line → Linear (constant distance, so speed = 0)
- d) ✔ Straight line (negative slope) → Linear
- e) ✘ Curved → Non-linear
- f) ✘ Curved → Non-linear

> Note: Even though graph (c) shows no movement, it is still a linear relationship because distance doesn't change with time — it's a constant function, which is a special case of a linear function.

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✔ Final Answer:

The graphs that show linear relations between distance and time are:
a), c), and d)

🔍 Justification:

- Linear relationships appear as straight lines on a distance-time graph.
- Graphs a) and d) have straight lines with constant slopes (positive and negative respectively), showing constant speed.
- Graph c) is a horizontal straight line, representing zero speed (no motion), but still a linear relationship since distance is constant over time.
- Graphs b), e), f) are curved, indicating changing speed, hence non-linear.

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✔ Answer to Question 2:
Graphs a), c), and d) show linear relations because they are straight lines, indicating a constant rate of change (or zero rate) between distance and time.