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Given a position vs. time graph, all sorts of analyses can be done. The slope through two points on the graph represents the change in position over the change in time, or the velocity. More precisely, this is equal to dx/dt where x models position and t is time. This is known as the derivative of the function.
Moreover, we can take d2x/dt2 (the second derivative) to obtain acceleration, another useful thing to know.
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Professor
Beau
CoachThe important characteristics of a position-time graph are the slope, which represents the object's velocity, and the shape of the curve, which indicates the object's motion (constant velocity, acceleration, deceleration, or at rest). The x-intercept of the graph represents the initial position of the object.
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What is position - time graph?
A position-time graph shows the relationship between an object's position and time. The position of the object is typically plotted on the y-axis, while time is on the x-axis. The slope of the graph represents the object's velocity, with a steeper slope indicating a higher velocity.
Is The slope on a position-time graph is representative of the acceleration of the object?
No, the slope on a position-time graph represents the object's velocity, not acceleration. Acceleration would be represented by the slope of the velocity-time graph.
How to convert a velocity time graph into a position time graph?
The position at time t (and therefore the height of the p-t graph) will be the area under the v-t curve between time 0 and t.
What information can be learned from a position-time graph and from a speed-time graph?
A position time graph can show you velocity. As time changes, so does position, and the velocity of the object can be determined. For a speed time graph, you can derive acceleration. As time changes, so does velocity, and the acceleration of the object can be determined.If you are plotting velocity (speed) versus time, the slope is the acceleration.
How do you go from a position graph to a velocity graph?
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.
