What is the difference between a horizontal line on a distance-time graph and a horizontal line on a velocity-time graph?

On a distance-time graph, a horizontal line means the object is stationary (speed = 0). On a velocity-time graph, a horizontal line means the object is moving at a constant, non-zero velocity.

How does a distance-time graph distinguish between constant speed and acceleration?

Constant speed is shown as a straight diagonal line with a fixed gradient. Acceleration is shown as a curve where the gradient (steepness) increases over time.

When comparing two straight lines on the same distance-time graph, how do you determine which object is faster?

The object represented by the steeper line is faster. A steeper gradient indicates that more distance is covered in the same amount of time compared to a shallower line.

What common mistake do students make when they see a horizontal line on a distance-time graph?

Students often assume the object is moving at a 'steady speed' because the line is straight. However, because the distance is not changing, the object is actually at rest (stationary).

Why is it an error to calculate speed using only one point $(x, y)$ from the graph?

Speed is the gradient, which is the *change* in distance over the *change* in time. Using one point assumes the object started at $(0,0)$, which may not be true if the graph has a non-zero y-intercept.

What error occurs if you ignore the units on the axes when calculating speed?

You may calculate a numerical value that is technically correct for the units shown (e.g., km/min) but incorrect for standard scientific reporting (m/s), leading to massive scale errors.

Define the 'gradient' of a distance-time graph.

The gradient is the ratio of the vertical change (distance) to the horizontal change (time). In physics, this gradient is equal to the speed of the object.

What is the formula for calculating speed from a distance-time graph?

The formula is $speed = \frac{y_2 - y_1}{x_2 - x_1}$, where $y$ represents distance and $x$ represents time. This is equivalent to calculating the gradient of the line.

How is 'Average Speed' calculated for an entire journey shown on a graph?

Average speed is the total distance (the final y-value if the object didn't return) divided by the total time (the final x-value). It averages out all speeds and stationary periods.

What does a downward-sloping line (negative gradient) represent?

It represents an object moving back toward its starting position. The distance from the origin is decreasing as time increases.

Distance-Time Graphs | Pearson Edexcel GCSE Physics

Distance-Time Graphs

Summary

Distance-time graphs are visual representations used to describe the motion of an object along a straight path. By plotting distance on the vertical axis and time on the horizontal axis, these graphs allow for the determination of an object's position, speed, and state of motion at any given moment.

1. Definition & Core Concepts

A distance-time graph illustrates the relationship between the distance an object has traveled from a fixed starting point and the time elapsed during the journey.
The horizontal axis (x-axis) always represents time ( $t$ ), which is the independent variable, typically measured in seconds (s), minutes (min), or hours (h).
The vertical axis (y-axis) represents distance ( $d$ ), the dependent variable, usually measured in meters (m) or kilometers (km).
Every point on the line represents the specific distance an object has reached at a particular moment in time.

A distance-time graph showing three phases: constant speed (upward slope), stationary (horizontal line), and returning to the start (downward slope).

2. The Significance of Gradient

The gradient (or slope) of the line on a distance-time graph represents the speed of the object.
A steeper gradient indicates a higher speed, as the object is covering more distance in the same amount of time.
A shallower gradient indicates a lower speed, showing that the object is moving more slowly.
A negative gradient (sloping downwards) indicates that the object is moving back toward its starting position.

3. Interpreting Graph Shapes

Straight Diagonal Line: Represents motion at a constant speed. The speed does not change as long as the line remains straight.
Horizontal Line: Indicates that the object is stationary. Since the distance from the starting point is not changing as time passes, the speed is zero.
Curved Line: Represents changing speed. If the curve gets steeper (increasing gradient), the object is accelerating; if it gets flatter (decreasing gradient), the object is decelerating.

4. Methods & Calculations

5. Key Distinctions

6. Exam Strategy & Common Pitfalls