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

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

How does the calculation of 'total distance' differ between a distance-time graph and a velocity-time graph?

On a distance-time graph, the total distance is the final value on the y-axis. On a velocity-time graph, the total distance is the total area enclosed between the graph line and the time axis.

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

The object with the steeper gradient (slope) is moving faster because it covers more distance in the same amount of time.

What is a common mistake when calculating acceleration from a velocity-time graph with a downward sloping line?

Students often forget to include a negative sign. A downward slope represents deceleration, which is a negative acceleration value ($a < 0$).

Why is it incorrect to say an object is 'stopped' just because the line on a velocity-time graph is flat?

A flat line only means the velocity is not changing. If the flat line is above the x-axis (e.g., at $5 m/s$), the object is still moving, just not accelerating.

What error occurs if you use the 'final y-value' to find distance on a velocity-time graph?

The final y-value only tells you the final velocity. To find distance on a velocity-time graph, you must calculate the area under the line, not just look at the final point.

Define 'Gradient' in the context of a motion graph.

The gradient is the steepness of the line, calculated as the change in the vertical axis divided by the change in the horizontal axis ($\frac{\Delta y}{\Delta x}$).

What does the area under a velocity-time graph represent?

The area under the graph represents the total displacement or distance traveled by the object during the given time period.

What is the formula for calculating constant acceleration from a velocity-time graph?

Acceleration ($a$) is the gradient: $a = \frac{v - u}{t}$, where $v$ is final velocity, $u$ is initial velocity, and $t$ is time taken.

If a distance-time graph is curved upwards (getting steeper), what does this tell you about the object's motion?

It indicates that the speed is increasing over time, meaning the object is accelerating.

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Graphs of Motion

Summary

Graphs of motion provide a visual representation of how an object's position or velocity changes over time. By analyzing the shape, gradient, and area of these graphs, one can determine fundamental kinematic quantities such as speed, velocity, acceleration, and total distance traveled.

1. Definition & Core Concepts

Graphs of motion are coordinate plots where time ( $t$ ) is typically represented on the horizontal x-axis, and a kinematic variable like distance ( $d$ ), displacement ( $s$ ), or velocity ( $v$ ) is on the vertical y-axis.
The gradient (slope) of a motion graph represents the rate of change of the y-axis variable with respect to time, providing immediate information about the object's motion state.
These graphs allow for the distinction between scalar quantities (like distance and speed) and vector quantities (like displacement and velocity), which account for direction.

2. Distance-Time Graphs

In a distance-time graph, the vertical axis represents the total distance covered from a starting point. A straight, diagonal line indicates that the object is moving at a constant speed.
The gradient of the line is numerically equal to the speed of the object; a steeper slope indicates a higher speed, while a shallower slope indicates a lower speed.
A horizontal line on this graph signifies that the distance is not changing over time, meaning the object is stationary (speed = 0).
Curved lines indicate changing speed; an increasing gradient (getting steeper) represents acceleration, while a decreasing gradient (flattening out) represents deceleration.

A distance-time graph showing three phases: a straight diagonal line for constant speed, a horizontal line for stationary state, and an upward curve for acceleration.

3. Velocity-Time Graphs

4. Methods & Techniques

5. Key Distinctions

6. Exam Strategy & Tips