Wouldn't the legitimate formula be v2-v1 instead? In this formula, if the frame of reference is moving faster, the object in front appears to have a positive velocity? It seems as though this may be written incorrectly.

I don't understand very well what you mean. Actually that last formula is derived from the equation of conservation of kinetic energy. KA has two videos, one showing the very long way and shorter way. If you use that formula, your equations will be much less tedious and doing a system of equations with the momentum one will give you the result you are searching for this type of problems where momentum and energy is conserved (ellastic collision). The frame of reference doesn't move... I just think it's poorly worded. If you can please be more clear, if I'm capable, I would be happy to help. What drove you into that conclusion? You seem to have upvotes and so maybe I'm the only one who doesn't understand the question...

Im confused about relative velocity, I can see how the principle would work with objects of equal mass, but not different mass.

Well first of all velocity doesn't depend on the mass which is insane. Could you develop more your question? If you plug in the equations is going to give you the desired result. Remeber that we are talking about ellastic collisions where both kinetic energy and momentum are conserved.

What is the difference between impulse and momentum?

Impulse is defined as the change in momentum. Hope this helps!

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Class 11 Physics (India) - Hindi

Course: Class 11 Physics (India) - Hindi > Unit 4

Lesson 9: Elastic and inelastic collisions (Hindi)

Elastic collisions review

Google Classroom

Review the key concepts, equations, and skills for elastic collisions, including how to predict objects' final velocities.

Key terms

Term (symbol)	Meaning
Closed system	System that is not acted on by a net external force. Also called an isolated system.
Conservation of momentum	In a closed (isolated) system, momentum is constant.
Elastic collision	Collision where both momentum and kinetic energy are conserved. There is no change in kinetic energy in the system as a result of the collision.

Equations

Equation	Symbols	Meaning in words
p, start subscript, i, end subscript, equals, p, start subscript, f, end subscript	p, start subscript, i, end subscript and p, start subscript, f, end subscript are the total initial and final momentum	The total initial momentum equals the total final momentum for a closed system. Commonly called the conservation of momentum.

[What does the full conservation of momentum equation look like for two colliding objects?]

How to predict final velocities for an elastic collision

We know a collision is elastic if kinetic energy is conserved:

start fraction, 1, divided by, 2, end fraction, m, start subscript, 1, end subscript, v, start subscript, 1, i, end subscript, squared, plus, start fraction, 1, divided by, 2, end fraction, m, start subscript, 2, end subscript, v, start subscript, 2, i, end subscript, squared, equals, start fraction, 1, divided by, 2, end fraction, m, start subscript, 1, end subscript, v, start subscript, 1, f, end subscript, squared, plus, start fraction, 1, divided by, 2, end fraction, m, start subscript, 2, end subscript, v, start subscript, 2, f, end subscript, squared

and momentum is conserved:

m, start subscript, 1, end subscript, v, start subscript, 1, i, end subscript, plus, m, start subscript, 2, end subscript, v, start subscript, 2, i, end subscript, equals, m, start subscript, 1, end subscript, v, start subscript, 1, f, end subscript, plus, m, start subscript, 2, end subscript, v, start subscript, 2, f, end subscript

If we imagine ourselves sitting on object 1 moving at velocity v, start subscript, 1, end subscript, object 2 will look like it is moving at speed v, start subscript, 1, end subscript, minus, v, start subscript, 2, end subscript. The difference in the velocities of the two objects tells us how fast object 1 is moving relative to object 2, and is sometimes called the relative velocity. If kinetic energy and momentum are conserved, we can make some predictions about the relative velocity before and after the collision.

The magnitude of the relative velocity is the same before and after the collision. That means if we are sitting on object 1 moving at velocity v, start subscript, 1, end subscript, object 2 will look like it is moving at the same speed both before and after the collision.

vertical bar, v, start subscript, 1, i, end subscript, minus, v, start subscript, 2, i, end subscript, vertical bar, equals, vertical bar, v, start subscript, 1, f, end subscript, minus, v, start subscript, 2, f, end subscript, vertical bar

The relative velocity has opposite signs before and after the collision. If we are sitting on object 1 moving at v, start subscript, 1, end subscript, object 2 will look like it changes direction after the collision.

v, start subscript, 1, i, end subscript, minus, v, start subscript, 2, i, end subscript, equals, minus, left parenthesis, v, start subscript, 1, f, end subscript, minus, v, start subscript, 2, f, end subscript, right parenthesis

The relative velocity will have these properties before and after an elastic collision for any combination of masses.

Common mistakes and misconceptions

Sometimes people forget that momentum is always conserved, but only in an isolated system. If there is a net external force on the system (an external impulse), then momentum is added to the system, and momentum is not conserved.

Learn more

For an overview on momentum, read our article on the conservation of momentum.

For deeper explanations of conservation of momentum and elastic collisions, see a worked example video on bouncing fruit and an ice skater throwing a ball.

To check your understanding and work toward mastering these concepts, check out our exercise on finding speed and mass using the conservation of momentum.

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Joshua
Posted 3 years ago. Direct link to Joshua's post “Let us say I am on object...”
Let us say I am on object A moving 5 m/s in the positive direction(defined as to the right on the page in this case) and object B is moving 3 m/s also to the right and I decided to calculate relative velocity the same way in the article I would take v1( 5 m/s) and subtract v2(3 m/2) from it this leaves me with a positive 2 m/s. This means I would see object b moving to the right at a speed of 2 m/s relative to me. If you go based on intuition this can't be right as you should see object b moving away from you due to its lower speed. and it would be moving away at a velocity of -2 m/2
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(7 votes)
Answer
- Anshari Hasanbasri
  Posted 2 years ago. Direct link to Anshari Hasanbasri's post “Remember that the 2 m/s y...”
  Remember that the 2 m/s you got represents how fast you are moving (on object A) relative to object B. In other words, if your friend was on object B, she would see you moving 2 m/s away from her (not her from you).
  
  If you wanted to calculate how fast object B is moving away from you, then you would swap the numbers: (3-5) = -2 m/s (which satisfies your intuition).
  
  Hope this helps.
  Comment on Anshari Hasanbasri's post “Remember that the 2 m/s y...”
  (1 vote)
eli.weber
Posted 3 years ago. Direct link to eli.weber's post “Wouldn't the legitimate f...”
Wouldn't the legitimate formula be v2-v1 instead? In this formula, if the frame of reference is moving faster, the object in front appears to have a positive velocity? It seems as though this may be written incorrectly.
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(6 votes)
Answer
- pa_u_los
  Posted 3 years ago. Direct link to pa_u_los's post “I don't understand very w...”
  I don't understand very well what you mean. Actually that last formula is derived from the equation of conservation of kinetic energy. KA has two videos, one showing the very long way and shorter way. If you use that formula, your equations will be much less tedious and doing a system of equations with the momentum one will give you the result you are searching for this type of problems where momentum and energy is conserved (ellastic collision). The frame of reference doesn't move... I just think it's poorly worded. If you can please be more clear, if I'm capable, I would be happy to help. What drove you into that conclusion? You seem to have upvotes and so maybe I'm the only one who doesn't understand the question...
  Button navigates to signup page
  (2 votes)
Shu-Mang Feng
Posted 4 years ago. Direct link to Shu-Mang Feng's post “Im confused about relativ...”
Im confused about relative velocity, I can see how the principle would work with objects of equal mass, but not different mass.
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(4 votes)
Answer
- pa_u_los
  Posted 3 years ago. Direct link to pa_u_los's post “Well first of all velocit...”
  Well first of all velocity doesn't depend on the mass which is insane. Could you develop more your question? If you plug in the equations is going to give you the desired result. Remeber that we are talking about ellastic collisions where both kinetic energy and momentum are conserved.
  Button navigates to signup page
  (2 votes)
mohamad
Posted 4 years ago. Direct link to mohamad's post “Why The magnitude of the ...”
Why The magnitude of the relative velocity is the same before and after the elastic collision?
Button navigates to signup pageComment on mohamad's post “Why The magnitude of the ...”
(3 votes)
Answer
vivian Xia
Posted 2 years ago. Direct link to vivian Xia's post “What is the difference be...”
What is the difference between impulse and momentum?
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(2 votes)
Answer
- obiwan kenobi
  Posted 2 years ago. Direct link to obiwan kenobi's post “Impulse is defined as the...”
  Impulse is defined as the change in momentum. Hope this helps!
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  (3 votes)
CamilleJ
Posted 8 months ago. Direct link to CamilleJ's post “after an elastic collisio...”
after an elastic collision, what happens to the velocity of each car?
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(2 votes)
Answer