GCSE Physics Tutorial: Calculating Speed from the Gradient of a Distance-Time Graph
Distance-time graphs offer a wealth of information about an object's motion, including its speed. By analysing the gradient (slope) of a distance-time graph, you can calculate the speed of the object. In this tutorial, we'll explore how to calculate speed from the gradient of a distance-time graph and understand the relationship between the two.
The Relationship between Gradient and Speed
In a distance-time graph, the gradient (slope) of the line represents the rate of change of distance with respect to time. Mathematically, the gradient is calculated as:
Gradient = Change in Distance / Change in Time
For an object moving at a constant speed, the distance-time graph is a straight line. The gradient of this line is equal to the speed of the object.
Steps to Calculate Speed from Gradient
To calculate the speed of an object from the gradient of a distance-time graph, follow these steps:
Identify the Line Segment: Determine the section of the graph that corresponds to the object's motion at a constant speed. This will be a straight line.
Choose Two Points: Select two points on the line segment. These points should be clearly defined on the graph, such as where the line intersects gridlines.
Calculate Change in Distance and Time: Find the change in distance (vertical difference) and the change in time (horizontal difference) between the two selected points.
Calculate Speed: Divide the change in distance by the change in time to calculate the speed.
Example Calculation
Let's say you have a distance-time graph with a straight line segment between points A and B. The change in distance between A and B is 200 meters, and the change in time is 20 seconds. To calculate the speed:
Gradient (Speed) = Change in Distance / Change in TimeSpeed = 200 m / 20 s = 10 m/s
The speed of the object is 10 meters per second.
Summary
Calculating speed from the gradient of a distance-time graph involves determining the slope of the line that represents the object's motion at a constant speed. By selecting two points on the line and calculating the change in distance and time between them, you can directly compute the speed. Understanding this relationship allows you to interpret distance-time graphs and extract valuable information about an object's motion without needing to use complex equations.
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