Question

A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statements about the velocity of the car is true?
A. Magnitude of velocity is constant
B. Both magnitude and direction of velocity change
C. Velocity is directed towards the centre of the circle
D. Magnitude of velocity is constant but direction changes

Answer 1

Hint: Before we start addressing the problem, we need to know about uniform motion. When an object travels in a straight line, then covers equal distances in equal intervals of time. Then this is called uniform motion.

Complete step by step solution:
Consider that a car is moving in a circular motion. While it is travelling in a circular motion, it covers equal angles from the centre and in equal intervals of time, this means it is travelling in a uniform motion. Since it covers equal angles, its angular speed is constant. Hence, the linear speed is also constant, which means, the magnitude of velocity is constant, but the direction keeps changing.

Then the angular velocity is perpendicular to the plane of the circle and therefore the angle between the angular velocity and linear velocity is \[{90^0}\]. Therefore, the magnitude of the velocity of the car is constant but the direction changes.

Hence, option D is the correct answer.

Note:In this problem it is important to remember that when a car travels with equal angles in equal intervals of time, that is it has a uniform motion. So only the direction of the car changes, not the magnitude of velocity.