The graph of position with respect to time is offered to visualize the activity of an object. The slope of the position vs time graph provides the velocity the the object at a certain time.

The slope of a place vs time graph to represent the velocity the the object. So in ~ a offered moment, the slope mirrors the object's velocity at that point. Remember the velocity is a vector quantity. It way it has both magnitude and direction. The size of velocity is additionally termed together speed. Because this is only involved with objects moving in a straight line, the just two direction that must be tackled space forward and also backward. If the velocity is positive, climate the displacement that the object is in front direction. If the velocity is negative, then the displacement of the thing is in backward.

You are watching: What does the slope of a position time graph measure

Before knowledge the steep of position-time graph in detail, that is vital to understand the slope.

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## Slope key Points

·The larger the slope, the steeper the line.

·A line that that moves up and also to the ideal represents a hopeful slope. In various other words, in a hopeful slope, as x increases, y additionally increases, as displayed below:

·A line that moves down and to the ideal represents a negative slope. In other words, in a negative slope, as x increases, y decreases, as displayed below:

·The horizontal line represents a zero slope.

·For a upright line, the slope is undefined.

## Reading position vs Time Graph

Usually because that graphs to it is in plotted in XY-plane, the independent change in the graph is stood for on the horizontal axis and the dependent variable is represented on the vertical axis.

In Position-Time graph, Time is the independent variable and also displacement of the thing is the dependent variable which counts on time. The upright axis to represent the place of the object and the horizontal axis represents the time taken by the object. The steep is identified as increase over Run. “Rise” is the adjust in place with time i beg your pardon is additionally referred as displacement and “Run” is the readjust in time. Therefore, steep in place vs Time Graph represents the readjust in place over the change in time i beg your pardon is also called velocity. Hence, slope to represent the velocity of things in position vs Time Graph.

## Interpretation of position vs Time Graph based on the slope

•Position vs Time Graph with Zero Slope: If the position vs Time graph for things at remainder is plotted, it will certainly be a horizontal line for which steep is zero. It indicates that the velocity the the object is zero.

•Position vs Time Graph having actually a consistent and optimistic Slope: If the position vs Time graph for an object that is relocating with uniform speed in forward direction is plotted, it will certainly be a right line v a confident slope. It indicates that the velocity of the object is constant and the is moving in front direction. Because that a straight-line graph of position, the slope to represent the mean velocity that the object.

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•Position vs Time Graph having actually a continuous and an unfavorable Slope: If the place vs Time graph for an item that is moving with uniform speed but in backward direction is plotted, it will be a directly line with an unfavorable slope. It suggests that the velocity the the thing is constant and the thing is relocating in backward direction. For a straight-line graph the position, the slope to represent the typical velocity the the object.

•Position vs Time Graph having actually a Varying and also Positive Slope: Both the graphs call you the the thing is accelerating because the line is in the form of a curve and is going up. Since the steep is changing at every circumstances which suggests that speed is an altering with time and also the adjust of rate with time is referred to as acceleration.

Here, the slope of the tangent drawn at any suggest to the curve provides the instantaneous velocity of the object.

Hence, it can be provided that the shape of the heat on the position time graph (straight, curving, steeply sloped, mildly sloped, etc.) explains various information around the movement of the object.

## Keep Learning

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Vector NotationConstant AccelerationConstant Acceleration In One DimensionExample troubles Of Projectile MotionFrame of ReferenceAcceleration together A Vector QuantityInstantaneous SpeedInstantaneous Velocity native Position-Time Graph