Question

Can displacement time graph have a negative slope? When?

Answer 1

It is a matter of sign convention. If movement in one direction is regarded as positive distance, then movement in the opposite direction would be negative distance. A yo-yo is a good example: If movement downward is regarded as positive, then distance from your hand to the yo-yo is increasing as the yo-yo moves toward the end of the string. At that point the yo-yo starts upward and the distance to your hand is decreasing - which is negative distance traveled in this convention. The graph in this case would resemble a triangle