When it comes to physics, it’s important to understand the difference between speed and velocity. While speed refers to the distance traveled by an object in a given amount of time, velocity includes both the speed and the direction of the object’s movement.
Now, the question is whether it’s possible for a particle to have a non-zero velocity throughout an interval but still have an average velocity of zero over that interval.
The Basics of Velocity and Average Velocity
To answer the above question, let’s first take a look at what velocity and average velocity actually mean.
Velocity is a vector quantity that includes both the speed and direction of motion. When we talk about the velocity of an object, we’re referring to how fast it’s moving in a particular direction. For example, a car driving at 60 miles per hour due north has a velocity of 60 miles per hour in the north direction.
Average velocity, on the other hand, is calculated by dividing the displacement (change in position) of an object over a given time interval by the time interval itself. This means that if the average velocity of a particle is zero over a particular interval, then its net displacement is zero during that interval.
Understanding the Situation
Now that we know the basics of velocity and average velocity, let’s take a closer look at the scenario in question.
Suppose we have a particle that’s moving in a particular direction throughout a given time interval. According to our book, if the particle’s speed is never zero over that interval, then its average speed can’t be zero either.
So, the question is whether velocity behaves the same as speed in this situation.
Answering the Question
The answer is no, it’s not possible for a particle to have a non-zero velocity throughout an interval but still have an average velocity of zero over that interval.
To understand why, let’s think about it like this: If a particle has a non-zero velocity, that means it’s moving in a particular direction. For the particle’s average velocity to be zero over a particular interval, it would have to move the same distance in the opposite direction as it did in the original direction.
This would mean that the particle’s net displacement over the interval is zero, which implies that the particle’s final position is the same as its initial position. If this is the case, then the particle must have come to a complete stop at some point during the interval, meaning its velocity was zero at that moment.
Example
Let’s look at an example to make this clearer. Suppose a particle is moving in a particular direction at a constant velocity of 10 meters per second for 10 seconds.
If we calculate the average velocity of the particle over the entire 10-second interval, we get:
Since the particle’s net displacement over the entire interval is zero, its average velocity is also zero.
However, if we look at the particle’s velocity at any given moment during the interval, we see that it’s always 10 meters per second in the same direction.
This means that the particle’s velocity is never zero over the interval, but its average velocity over the same interval is still zero since its net displacement over the entire interval is zero.
Conclusion
In conclusion, while it’s not possible for a particle to have a non-zero speed throughout an interval but still have an average speed of zero, the same cannot be said for velocity. A particle can have a non-zero velocity throughout an interval, but its average velocity over that interval would still be zero only if its net displacement over the interval is zero.
Is it Possible to Have a Situation In Which Velocity of the Particle is Never 0 But Its Average Velocity In an Interval is 0?
When it comes to physics, it’s important to understand the difference between speed and velocity. While speed refers to the distance traveled by an object in a given amount of time, velocity includes both the speed and the direction of the object’s movement.
Now, the question is whether it’s possible for a particle to have a non-zero velocity throughout an interval but still have an average velocity of zero over that interval.
The Basics of Velocity and Average Velocity
To answer the above question, let’s first take a look at what velocity and average velocity actually mean.
Velocity is a vector quantity that includes both the speed and direction of motion. When we talk about the velocity of an object, we’re referring to how fast it’s moving in a particular direction. For example, a car driving at 60 miles per hour due north has a velocity of 60 miles per hour in the north direction.
Average velocity, on the other hand, is calculated by dividing the displacement (change in position) of an object over a given time interval by the time interval itself. This means that if the average velocity of a particle is zero over a particular interval, then its net displacement is zero during that interval.
Understanding the Situation
Now that we know the basics of velocity and average velocity, let’s take a closer look at the scenario in question.
Suppose we have a particle that’s moving in a particular direction throughout a given time interval. According to our book, if the particle’s speed is never zero over that interval, then its average speed can’t be zero either.
So, the question is whether velocity behaves the same as speed in this situation.
Answering the Question
The answer is no, it’s not possible for a particle to have a non-zero velocity throughout an interval but still have an average velocity of zero over that interval.
To understand why, let’s think about it like this: If a particle has a non-zero velocity, that means it’s moving in a particular direction. For the particle’s average velocity to be zero over a particular interval, it would have to move the same distance in the opposite direction as it did in the original direction.
This would mean that the particle’s net displacement over the interval is zero, which implies that the particle’s final position is the same as its initial position. If this is the case, then the particle must have come to a complete stop at some point during the interval, meaning its velocity was zero at that moment.
Example
Let’s look at an example to make this clearer. Suppose a particle is moving in a particular direction at a constant velocity of 10 meters per second for 10 seconds.
If we calculate the average velocity of the particle over the entire 10-second interval, we get:
Since the particle’s net displacement over the entire interval is zero, its average velocity is also zero.
However, if we look at the particle’s velocity at any given moment during the interval, we see that it’s always 10 meters per second in the same direction.
This means that the particle’s velocity is never zero over the interval, but its average velocity over the same interval is still zero since its net displacement over the entire interval is zero.
Conclusion
In conclusion, while it’s not possible for a particle to have a non-zero speed throughout an interval but still have an average speed of zero, the same cannot be said for velocity. A particle can have a non-zero velocity throughout an interval, but its average velocity over that interval would still be zero only if its net displacement over the interval is zero.