Can instantaneous velocity be different from average velocity?

[kolade]

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

 

[kuruman]

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?

 

[kolade]

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

 

[kuruman]

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?

 

[kolade]

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

 

[kuruman]

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?

 

[kolade]

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

 

[kuruman]

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?

 

[kolade]

It's going to be the same because there is no change in acceleration

 

[kuruman]

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?

 

[kolade]

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?

 

[kuruman]

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?