# A particle moves along the x axis with a displacement versus time as shown in Fig, Roughly sketch curves of velocity versus time and acceleration versus time for this motion.

Navjyot Kalra
8 years ago
The displacement-time graph is shown below:

It is important to note that at points A, B and C, the slope of the displacement-time graph will be equal to zero. Therefore the velocity corresponding to these points must be zero.
Also, the maximum negative change in displacement-time graph can be obtained about point D. Therefore the velocity-time graph has negative values in the vicinity and at point D. It is important to note that the slope of x versus t graph becomes positive when the curves moves to the right of point B.
Therefore one obtains a curve that accounts for the fact that the slope of displacement-time graph decreases from point A , reaches a maximum negative value (corresponding to point D), and increases once again to the right of point B as shown in the figure below:

It is important to note that from the beginning of time to point A in displacement-time graph the slope of decreases relative to its initial value.
The acceleration-time graph can be obtained in the same way by analyzing the velocity-time curve. The negative slope of the velocity-time graph up to point D ensures that the acceleration remains negative. But as soon as the velocity-time graph passes point D. The slope becomes positive and the acceleration-time curve must move from negative region to positive one and in a continuous fashion, as shown in the figure below:

As long as the change of velocity is positive, the acceleration will be on the positive side but when the velocity attains a maximum value just before point C, the acceleration becomes zero, and then decreases again in accordance with negative slope of velocity-time graph.