Draw `v to t` graph for constant velocity and explain it.

Explanation

Suppose, there is an object moving with constant velocity u. Its velocity-time graph is as shown in figure.

The `v gt t` curve is a straight line parallel to the time axis.
The area under it between t = 0 and I = T is the area of the rectangle of height u and base T.Therefore, area = uXT = UT which is the displacement in this time interval.
Note the dimensions of quantities on the two coordinate axes and it will give the proof.
The area enclosed above t-axis is positive and the area enclosed below t-axis is negative,
Note that the x-6, 0-t and a-t graphs shown in several figures in this chapter have sharp kinks at some points implying that the functions are not differentiable at these points.
In any realistic situation, the functions will be differentiable at all points and the graphs will be smooth.
What this means physically is that acceleration and velocity cannot change values abruptly at an instant. Changes are always continuous.