What is the fundamental difference between a horizontal line on a distance-time graph versus a speed-time graph?

On a distance-time graph, a horizontal line means the object is stationary (speed is zero). On a speed-time graph, a horizontal line means the object is moving at a constant speed (acceleration is zero).

How does the interpretation of a negative gradient differ between distance-time and speed-time graphs?

In a distance-time graph, a negative gradient means the object is moving back toward its starting position. In a speed-time graph, a negative gradient indicates the object is slowing down (decelerating).

When calculating average speed for a journey with multiple stops, should the 'rest' time be included in the 'total time'?

Yes, the total time must include all periods of rest. Average speed is defined as the total distance covered divided by the entire duration of the journey from start to finish.

What is a common mistake when calculating speed from a line segment that does not pass through the origin $(0,0)$?

A common error is dividing the y-coordinate by the x-coordinate of a single point. You must use the change in distance divided by the change in time ($\frac{\Delta d}{\Delta t}$) for that specific segment.

Why is it incorrect to say an object has 'negative speed' when the distance-time graph has a downward slope?

Speed is a scalar quantity and is always positive. The downward slope indicates a negative velocity (direction), but the speed is simply the steepness (absolute value) of that gradient.

What error occurs if you misinterpret the scale of the x-axis (e.g., treating each grid square as 10 minutes instead of 15)?

This leads to an incorrect 'run' value in the gradient calculation, resulting in an inaccurate speed. Always check the axis labels to determine the exact value of each grid increment.

What does the 'gradient' represent on a distance-time graph?

The gradient represents the speed of the object. It is calculated as the change in distance (rise) divided by the change in time (run).

Define 'Stationary' in the context of a distance-time graph.

Stationary means the object is at rest and not moving. On the graph, this is shown as a horizontal line where the distance remains constant as time passes.

What is the formula for Average Speed?

The formula is $Average\ Speed = \frac{Total\ Distance}{Total\ Time}$. It represents the constant speed required to cover the same distance in the same total duration.

If a distance-time graph is a curve rather than a straight line, what does this tell you about the object's speed?

A curve indicates that the speed is changing over time. The object is either accelerating (getting steeper) or decelerating (getting shallower).

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Distance-Time Graphs

Summary

Distance-time graphs are visual representations used to describe the motion of an object over a specific period. By plotting distance on the vertical axis and time on the horizontal axis, these graphs allow for the calculation of speed via the gradient and the interpretation of different states of motion, such as constant velocity, rest, or returning to a starting point.

1. Definition & Core Concepts

A Distance-Time Graph plots the total distance an object has traveled against the time elapsed. The vertical axis (y-axis) represents distance, while the horizontal axis (x-axis) represents time.
The position of any point on the line tells you exactly how far the object is from its starting reference point at a specific moment in time.
These graphs are fundamental in kinematics for visualizing journeys, identifying periods of movement versus rest, and comparing the relative speeds of different objects.

A distance-time graph showing three segments: a positive gradient (moving away), a horizontal line (stationary), and a negative gradient (returning to start).

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

Feature	Positive Gradient	Horizontal Line	Negative Gradient
Motion State	Moving away from start	Stationary (at rest)	Moving back toward start
Speed Value	Positive constant speed	Zero speed	Positive speed (direction is reversed)
Distance Change	Increasing	No change	Decreasing (relative to start)

Distance vs. Displacement: In basic distance-time graphs, a negative gradient usually implies returning to the origin. While the 'distance' from the start decreases, the total distance traveled by the object continues to accumulate for average speed calculations.

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions