Can a Body Have Constant Velocity and Varying Speed?

In physics, velocity and speed are both measures of motion, but they are distinct concepts:

• Speed is a scalar quantity that refers to how fast an object is moving, without regard to its direction.
• Velocity is a vector quantity, meaning it includes both the magnitude (how fast) and the direction of an object’s motion.

Given these differences, the question arises: Can a body have constant velocity and varying speed?

The Answer:

No, a body cannot have constant velocity and varying speed simultaneously. Here’s why:

1. Constant Velocity Means Constant Speed and Constant Direction

• If a body has constant velocity, both the speed and the direction of motion must remain constant over time.
• Velocity is a vector, which means that if the speed or the direction of motion changes, the velocity changes as well.
• Therefore, if the speed is changing, the velocity must also be changing, even if the direction remains constant.

Example:

Imagine you’re driving a car in a straight line. If you maintain a constant speed, but occasionally speed up or slow down, your speed is varying. Because velocity includes both speed and direction, the fact that your speed is changing means that your velocity is also changing, even if you’re still moving in the same direction.

2. Speed and Direction Changes Are Interrelated

In order for the velocity to remain constant, both the magnitude (speed) and direction of the motion must be unchanged. Even a small variation in speed will result in a change in velocity, because the magnitude of the velocity vector has changed.

Example of Constant Speed but Changing Velocity:

• Circular Motion: If an object moves in a circular path at a constant speed, the magnitude of the velocity (i.e., the speed) is constant, but the direction of the velocity changes continuously as the object moves along the circle.
• Although the speed is constant, the velocity is not constant because the direction of motion keeps changing. This is an example of uniform circular motion, where the speed remains constant, but the velocity changes due to the continuous change in direction.

Conclusion:

A body cannot have constant velocity and varying speed at the same time. For an object to have constant velocity, both its speed and direction must remain constant. Any change in speed will result in a change in velocity, even if the direction stays the same. Thus, if speed is varying, the velocity must also be varying.