Can instantaneous velocity be different from average velocity?

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Homework Help Overview

The discussion revolves around the relationship between instantaneous velocity and average velocity in the context of motion, specifically questioning whether they can differ when acceleration is zero.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the possibility of instantaneous velocity not being parallel to average velocity, particularly under conditions of zero acceleration. There are attempts to clarify definitions and implications of velocity in this context.

Discussion Status

The conversation is ongoing, with participants providing insights and asking clarifying questions. Some have suggested that when acceleration is zero, instantaneous and average velocities may be the same, while others are probing the reasoning behind this relationship.

Contextual Notes

Participants are working with the assumption that the definitions of average and instantaneous velocity are understood, but there is some uncertainty regarding the implications of zero acceleration on these velocities.

kolade
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Homework Statement


Is it possible for the instantaneous velocity of an object at some time, t1, to not be parallel to the average velocity over a short time interval, Δt=t2-t1? If it is not possible, explain why not. If it is possible, explain what this situation implies about the motion of the object.

Homework Equations

The Attempt at a Solution


i would say it's possible when acceleration is zero but I'm not sure
 
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kolade said:

Homework Statement


Is it possible for the instantaneous velocity of an object at some time, t1, to not be parallel to the average velocity over a short time interval, Δt=t2-t1? If it is not possible, explain why not. If it is possible, explain what this situation implies about the motion of the object.

Homework Equations

The Attempt at a Solution


i would say it's possible when acceleration is zero but I'm not sure

Are you saying that it is possible for the instantaneous velocity to not[/color] be parallel to the average velocity when the acceleration is zero?
 
kuruman said:
Are you saying that it is possible for the instantaneous velocity to not be parallel to the average velocity when the acceleration is zero?
yes but I'm not sure
 
kolade said:
yes but I'm not sure
OK, let's make sure you're sure. Please answer the following questions
1. What do you need to do to find the average velocity, i.e. what is an expression that will allow you to calculate it?
2. If an object has initial velocity v1 to the right at time t1 and its acceleration is zero, how will its velocity change at some later time t2?
3. Given (1) and (2) above, what is the average velocity of this object from time t1 to time t2?
 
kuruman said:
OK, let's make sure you're sure. Please answer the following questions
1. What do you need to do to find the average velocity, i.e. what is an expression that will allow you to calculate it?
2. If an object has initial velocity v1 to the right at time t1 and its acceleration is zero, how will its velocity change at some later time t2?
3. Given (1) and (2) above, what is the average velocity of this object from time t1 to time t2?
1) Δf/Δt
2)The velocity won't change because the acceleration which is the change in velocity is zero
3)i don't know how i can get this without the velocity and time
 
Two points for your answer in 1. (a) Velocity is a vector and so is average velocity. You don't show a vector equation; (b) What is the meaning of f in Δf/Δt?
Your answer in 2 is correct.
For 3 think again. If the velocity is v1 to the right at t1 and it doesn't change, what could it be at time t2?
 
kuruman said:
Two points for your answer in 1. (a) Velocity is a vector and so is average velocity. You don't show a vector equation; (b) What is the meaning of f in Δf/Δt?
Your answer in 2 is correct.
For 3 think again. If the velocity is v1 to the right at t1 and it doesn't change, what could it be at time t2?
velocity at t2 would still be the same if it does not change
 
kolade said:
velocity at t2 would still be the same if it does not change
Good. Now how do you think the instantaneous velocity compares with the average velocity when the acceleration is zero? If the two are the same, why are they? If they are different, in what way?
 
It's going to be the same because there is no change in acceleration
 
  • #10
kolade said:
It's going to be the same because there is no change in acceleration
That's not the reason. When the acceleration is zero, the average velocity is the same as the instantaneous velocity because something other than the acceleration is not changing. What is that?
 
  • #11
kuruman said:
That's not the reason. When the acceleration is zero, the average velocity is the same as the instantaneous velocity because something other than the acceleration is not changing. What is that?
Velocity?
 
  • #12
Are you asking me or are you telling me? See your answer 2 in post #5. OK, so we have found that, when the acceleration is zero, the instantaneous velocity vector is the same as the average velocity vector. Now answer this, what must be true for two vectors to be the same?
 

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