Figure shows the x-t plot of a particle in onc-dimensional...

Figure shows the $x$-t plot of a particle in onc-dimensional motion. Two different equal intervals of time are shown. Let $v_{1}$ and $v_{2}$ be average speed in time intervals 1 and 2 respectively. Then

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Key Concepts

Equal Time Intervals

Analyzing motion over equal time intervals helps isolate differences in speed or velocity since the constant time span means that any change in the slope (or displacement) directly reflects a change in the average speed or velocity of the object.

Slope of a Graph

The slope in an x-t graph represents the rate of change of position with respect to time, which corresponds to the velocity in one-dimensional motion. When comparing two different time intervals on the same graph, the slopes of the line segments directly indicate the comparative speeds during those intervals.

x-t Graph

An x-t graph plots the position of an object along a particular axis as a function of time. In one-dimensional motion, this graph is a critical tool for visualizing how the object's position changes, and its slope at any point gives information about the object's velocity at that time.

Average Speed

Average speed is defined as the total distance travelled divided by the time interval over which the motion occurs. In the context of an x-t graph, this is represented by the slope of a line segment connecting the starting and ending positions over the time interval.

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