0In kinematics, graph plays an important part in understanding various motions.
Commonly taught graphs for beginners are distance Vs time and displacement Vs time graph of rectilinear motion, in particular when an object is thrown vertically upwards.
The displacement Vs time graph in such a case is, a parabola mouth opening downwards. The derivative of this graph gives the value of velocity which gradually decreases to zero at its highest point then increases with a negative sign. But the double derivative which gives the value of acceleration remains constant throughout which is the value of g, i.e. acceleration due to gravity.
The shape of distance Vs time graph is a bit different. It remains same as that of displacement Vs time till first half then the curvature of the graph changes. Mathematically, such a point is called the point of inflexion where the curvature of graph changes. The important point to note here is that at the point of inflexion the double derivative is zero.
If we compare this graph with the previous one, the value of double derivative remains the same at all points except at the point of infection. It is so because the double derivative of distance Vs time graph gives "tangential acceleration". At the highest point, the velocity of the body is zero so is the value of tangential acceleration. A point which otherwise missed, if graphs are not studied properly.
