GCSE Physics Tutorial: Determining Speed from a Distance-Time Graph
Distance-time graphs offer a clear visual representation of an object's motion over time. By analysing the slope (gradient) of a distance-time graph, you can determine the speed of the object. In this tutorial, we'll guide you through the process of determining speed from a distance-time graph and understanding the relationship between the two.
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 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 Determine Speed from a Distance-Time Graph
To determine the speed of an object from a distance-time graph, follow these steps:
Identify a Straight Line Segment: Find a section of the graph where the object's motion is at a constant speed. This segment will be a straight line.
Select Two Points: Choose two points on the straight line segment. These points should be clearly defined on the graph, such as where the line intersects gridlines.
Calculate Change in Distance and Time: Determine 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 400 meters, and the change in time is 20 seconds. To determine the speed:
Gradient (Speed) = Change in Distance / Change in TimeSpeed = 400 m / 20 s = 20 m/s
The speed of the object is 20 meters per second.
Summary
Determining speed from a distance-time graph involves analysing the slope of the line that represents the object's motion at a constant speed. By selecting two points on the line, calculating the change in distance and time between them, and then dividing the distance by the time, you can determine the speed of the object. This method allows you to extract valuable information about an object's motion from the graph without needing complex equations.
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