Proof that v = u at on velocity time graph:

Velocity time graph is a graphical representation of the change in velocity with respect to time. It is a line graph plotted with velocity on Y-axis and time on X-axis. The slope of this graph gives the acceleration of the object.

Initial Velocity (u):
Initial velocity (u) is the velocity of the object at the start of the motion. It is represented by the point where the graph starts on the Y-axis.

Final Velocity (v):
Final velocity (v) is the velocity of the object at the end of the motion. It is represented by the point where the graph ends on the Y-axis.

Constant Velocity:
When the velocity time graph is a straight line parallel to the X-axis, it indicates that the object is moving with a constant velocity. This means the slope of the line is zero, and the acceleration is also zero.

Proof:
When an object moves with a constant velocity, its acceleration is zero. This means that there is no change in velocity with respect to time. Therefore, the final velocity (v) of the object will be the same as its initial velocity (u).

Hence, we can conclude that v = u at on velocity time graph when the object is moving with a constant velocity.