erive the equation for velocity-time relation (v = u + at) by graphical method.

Sure, here is the step-by-step derivation of the velocity-time relation (v = u + at) by graphical method:

1. Draw a velocity-time graph. The y-axis represents velocity (v) and the x-axis represents time (t).

2. Assume that the initial velocity of the object is 'u' at time t=0. So, plot a point on the y-axis at 'u'.

3. Assume that the object is moving with a constant acceleration 'a'. This means that the velocity of the object is increasing uniformly with time. So, the graph will be a straight line inclined to the time axis at an angle whose tangent is equal to 'a' (since acceleration is the slope of the velocity-time graph).

4. Now, let's consider any arbitrary time 't' on the x-axis. Draw a line from this point parallel to the y-axis until it intersects the graph. The point of intersection gives the velocity 'v' of the object at time 't'.

5. From the graph, you can see that the change in velocity from 'u' to 'v' is equal to the product of acceleration 'a' and time 't'. This is represented by the area of the rectangle formed by the y-axis, the x-axis, the line parallel to the y-axis at time 't', and the line on the graph from 'u' to 'v'.

6. Therefore, from the graph, we can derive the equation for velocity-time relation as v = u + at. This equation tells us that the final velocity 'v' of an object is equal to its initial velocity 'u' plus the product of its acceleration 'a' and the time 't' for which it has been moving.