Physics

Recall the key concepts related to position-time and velocity-time graphs and the condition for an object to return to its initial position:

In a position-time graph, if the object returns to its initial position, the final position value is equal to the initial position value. In a velocity-time graph, the displacement of the object is given by the area under the graph. If the object returns to its initial position, the net area under the graph (taking areas above the t-axis as positive and areas below the t-axis as negative) is zero.

 

Analyze each graph:

Graph A(position-time graph):

The initial position of the object is x = 0 at t = 0, and the final position at is also x = 0. So, the object returns to its initial position.

 

Graph B(velocity-time graph):

The area under the v - t graph from t = 0 to is a isosceles triangle with base and height , so its area . The net displacement (area under the graph) is non - zero, which means the object does not return to its initial position.

 

Graph C(velocity-time graph):

The area under the graph from t = 0 to is a rectangle with height and base , so . The area under the graph from to is a rectangle with height and base , so . The net displacement (area under the graph) is

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