To find the change in velocity of an aeroplane moving in a circular path after half a revolution, we can follow these steps:

Understand the Initial and Final Velocity

The aeroplane is moving in a circular path with a constant speed of .

At the start of the half revolution (let's denote this point as point A), the velocity vector can be represented as (assuming it is moving to the right along the x-axis).

Determine the Final Velocity

After half a revolution (point B), the aeroplane will be at the opposite side of the circular path. The direction of the velocity vector will now be opposite to the initial direction.

Thus, the final velocity vector can be represented as

.

Calculate the Change in Velocity

The change in velocity is given by the formula:

Substituting the values:

Interpret the Result

The magnitude of the change in velocity is in the direction opposite to the initial velocity.

Final Answer

The change in velocity in half of the revolution is .