Displacement Time Graphs
Displacement time graphs indicate the displacement relative to particular point as a vector. One direction is taken as positive and one direction is taken as negative, so only these this forwards and backwards motion can be displayed. At any time t the displacement can be read off the vertical axis by moving up from a certain time t to meet the graph then along to read off the displacement. For example the displacement at t=7 s below is 20 m.
General Points

The gradient at any point is equal to the rate of change of displacement, or the velocity. In particular a horizontal line has zero velocity or constant displacement.

At any time when the graph intercepts the t axis, the displacement AT THAT INSTANT is zero.

The area under an displacement time graph has no real meaning.

If the displacement is constant the graph of displacement against time is a horizontal line with the y – value equal to the displacement. The displacement illustrated in the graph below is 15 m.