In this question, we are given that an object is moving with a uniform acceleration "a". Its initial velocity is "u" and after time "t", its velocity becomes "v". We are asked about the shape of the velocity-time graph, specifically along the y-axis.

To understand this, let`s consider the equation of motion for the object: v = u + at

This equation states that the final velocity "v" is equal to the initial velocity "u" plus the product of acceleration "a" and time "t". If we rearrange this equation, we get:

v - u = at

This equation represents the equation of a straight line, where "v - u" is the displacement on the y-axis and "t" is the displacement on the x-axis. Therefore, the velocity-time graph will be a straight line.

Now, let`s analyze the options:

Option 1: Passing through origin - This means that the y-intercept is zero. However, the y-intercept in the equation v = u + at is u, not zero. Therefore, this option is incorrect.

Option 2: With x-intercept u - This means that the value of t where the graph intersects the x-axis is u. However, the x