Physics

Recall the relationship between velocity-time and position-time graphs:

The slope of a position-time graph gives the velocity of the object. In a velocity-time graph, the area under the curve gives the displacement of the object.

 

For the given velocity-time graph:

From t = 0 to , the velocity is a positive constant . This means the object is moving with a constant positive velocity, and the position-time graph should have a positive constant slope (a straight line with a positive slope). The displacement in this interval is .

 

From to , the velocity is 0. So, the object is at rest, and the position-time graph should be a horizontal line during this time interval.

 

From to , the velocity is a negative constant . This means the object is moving with a constant negative velocity, and the position-time graph should have a negative constant slope (a straight line with a negative slope). The displacement in this interval is .

 

The total displacement is: . So, the position-time graph should end up at a negative position.

 

Analyze each position-time graph:

Graph A

From

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