1. Does a car speedometer measure speed, velocity, or both?
2. Can an object have a varying speed if its velocity is constant? Can it have varying velocity if its speed is constant? If yes, give examples in each case.
3. When an object moves with constant velocity, does its average velocity during any time interval differ from its instantaneous velocity at any instant?
The Correct Answer and Explanation is :
- Does a car speedometer measure speed, velocity, or both?
A car’s speedometer measures speed, not velocity. Speed is a scalar quantity that indicates how fast an object is moving, without considering its direction. Velocity, on the other hand, is a vector quantity that includes both the magnitude (speed) and the direction of motion. Since a speedometer only shows how fast the car is moving, and doesn’t account for direction, it measures speed, not velocity.
- Can an object have a varying speed if its velocity is constant? Can it have varying velocity if its speed is constant? If yes, give examples in each case.
- Varying speed with constant velocity: No, if the velocity is constant, the speed must also be constant. Since velocity includes both magnitude (speed) and direction, any change in speed or direction would result in a change in velocity. Therefore, if the velocity is constant, there cannot be a varying speed.
- Varying velocity with constant speed: Yes, an object can have varying velocity while maintaining constant speed. For example, an object moving in a circular path at a constant speed, such as a car driving around a circular track, has a constant speed but a changing velocity because the direction of motion is continuously changing. Another example would be a point on the edge of a rotating wheel, where the speed remains constant, but the direction of the velocity vector is constantly changing.
- When an object moves with constant velocity, does its average velocity during any time interval differ from its instantaneous velocity at any instant?
No, when an object moves with constant velocity, its average velocity during any time interval does not differ from its instantaneous velocity at any instant. This is because the average velocity is calculated over a time interval and, in the case of constant velocity, it remains the same throughout that interval. Instantaneous velocity, on the other hand, is the velocity at a specific point in time. Since the object is moving with a constant velocity, the instantaneous velocity at any instant is identical to the average velocity over any time interval.
For an object moving with constant velocity, the magnitude and direction of velocity stay the same. As a result, the average velocity, which is the total displacement divided by the total time, is the same as the instantaneous velocity, which is the velocity at any specific moment in time. This consistency holds because, in both cases, the displacement occurs uniformly in both magnitude and direction. Therefore, there is no difference between the average and instantaneous velocities in this situation.