A section of a position–time graph has a gradient of +7 and another section has a gradient of −4. If the units on the graph are metres and seconds, and positive means south, what do these numbers mean about the motion being studied?
The gradient on a position-time plot is dx/dt , that is, the velocity (or rate of change of position with time).
In this case, the gradient of a section is +7 and or another section is -4. That is the velocity in the first section is 7 m/s and in the second section, it is -4 m/s.
Since the slopes are constant (+7 and -4), the velocity is constant in these two sections. that is there is no acceleration in the motion under study.
Since, positive denotes South in this case, the section with a positive slope (of +7) will have the particle moving to the south. For the negative slope, the particle is moving north (opposite of south direction).
Hope this helps.