Can a Body Have Constant Speed but Changing Velocity?
Yes, absolutely! This is one of the most fundamental concepts in kinematics, highlighting the critical distinction between speed and velocity.
The Core Difference
- Speed is a scalar quantity. It only describes how fast an object is moving (the magnitude).
- Velocity is a vector quantity. It describes both how fast an object is moving (speed) and in which direction it is traveling.
Since velocity depends on direction, a change in either speed OR direction will result in a change in velocity.
Why Velocity Changes with Constant Speed
If you are traveling at a constant speed, the magnitude part of your velocity vector remains unchanged. However, if your path is curved (even slightly), your direction is constantly changing. Because velocity is direction-dependent, the velocity vector is constantly changing. Therefore, the body is undergoing acceleration.
Illustrative Example: Uniform Circular Motion
Consider an athlete running at a constant speed of $5 \text{ m/s}$ around a circular track.
- Speed: Always $5 \text{ m/s}$. It never changes.
- Velocity: Because the runner is constantly turning to stay on the circular track, their direction is changing at every single point. Even though the magnitude is $5 \text{ m/s}$, the direction of the velocity vector is different at every moment.
Conclusion: The athlete has constant speed but changing velocity. This implies that even at constant speed, the object is accelerating (centripetal acceleration).