Question

position time graph for a particle moving with positive and negative velocities​

Answer 1

Negative Position-Time Graph with respect to Velocity

In position and time graphs, the slope of line indicates the velocity.

Therefore negative slope of a position-time graph actually indicates negative velocity.

Negative velocity is defined as the velocity of the object moving in an opposite direction.

Negative slope i.e in this case negative velocity does not mean that the velocity is decreasing.  

Graph of negative velocity need not move below the x-axis.

The following are the few examples of  a negative slope of a position -time graph.

The above image shows a negative slope i.e negative velocity in a position-time graph.

The graph goes gradually downward indicating the slow rate of negative velocity.