Question

An aeroplane is moving in a circular path with a speed of \(450\ \text{kmph}\). What is the change in velocity in half revolution?

• A. \(0\ \text{kmph}\)
• B. \(450\ \text{kmph}\)
• C. \(250\ \text{kmph}\)
• D. \(900\ \text{kmph}\)

Hint:

In half revolution of circular motion, velocity reverses direction, so change in velocity is \(2v\).

Answer 1

The Correct Option is D

Concept: Velocity is a vector quantity. In uniform circular motion, speed remains constant but direction of velocity changes continuously.

Step 1: Initial speed of the aeroplane is: \[ v=450\ \text{kmph} \]

Step 2: After half revolution, the aeroplane reaches the diametrically opposite point of the circle.
At this point, velocity direction becomes exactly opposite to the initial velocity. So: \[ \vec v_i=450 \] \[ \vec v_f=-450 \]

Step 3: Change in velocity: \[ \Delta v=\vec v_f-\vec v_i \] \[ \Delta v=-450-450 \] \[ \Delta v=-900 \] Magnitude of change in velocity: \[ |\Delta v|=900\ \text{kmph} \] Therefore, \[ \boxed{900\ \text{kmph}} \]