Position time graph is useful only in the case of 1D motion, you can't made a x-t graph for 3D motion (try ;) ). You need extra efforts to do this because you need a time refrence.
So position time graph is valuable for straight line (sometimes 2D) motion only, not for 3D.
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Limitations of a position vs. time graph include the inability to show changes in velocity or acceleration directly, as these quantities are not explicitly represented on the graph. Additionally, position vs. time graphs do not provide insight into the direction of motion or the underlying causes of the motion depicted. They are limited in capturing complex motion patterns that involve varying speeds or sudden changes in direction.
Motion can be represented graphically using position-time graphs, velocity-time graphs, and acceleration-time graphs. These graphs provide information about how an object's position, velocity, and acceleration change over time. Position-time graphs show the object's position at different times, velocity-time graphs show how the velocity changes over time, and acceleration-time graphs show how the acceleration changes over time.
The slope of a line drawn tangent to a point on a position vs. time graph represents the instantaneous velocity of the object at that point. It describes how the position of the object is changing at that exact moment in time.
When two objects have the same velocity on a position graph, their position vs. time graphs will have parallel lines with the same slope. This indicates that both objects are covering the same distance in the same amount of time, resulting in the same velocity.
To go from a position graph to a velocity graph, you can calculate the slope of the position graph at each point. The slope at any given point on a position vs. time graph represents the velocity at that specific time. Therefore, the velocity graph would be a plot of the slopes at each point on the position graph.
Acceleration can be determined from a position vs. time graph by finding the slope of the velocity vs. time graph. The slope of the velocity vs. time graph represents the rate at which velocity is changing, which is acceleration. A steeper positive slope indicates a higher acceleration, while a steeper negative slope indicates deceleration.