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Core 3.31 MAIN PAGE


Constant Acceleration
Free Fall
Forces and Newton's Law
Kinetic Energy
Potential Energy



Free Fall
Conservation of Energy
Conservation of Momentum


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Classic Problem in
Conservation of Momentum

Here is an example of a typical question in the area of Conservation of Momentum that students have difficulty solving:

There are two identical cars on the road moving toward each other. The first car moves with an initial velocity of 15 m/s towards the second car, which moves with an initial velocity of 10 m/s. The two cars collide and start moving together. Calculate the velocity of the movement of the two cars after the collision (this is called their final velocity).

Two cars colliding


Find the velocity of the movement of the two cars after the collision.

In order to solve this problem we have to find the final speed of both cars after they collide. We can do this by applying the law of conservation of momentum, which states that the sum of the initial momentums of the two cars before they collide is equal to the sum of the two cars' final momentum after the collision.


The first thing we must do is write down the formula for conservation of momentum.

Click on any part of the equation below to learn more about it.

 In this problem, before we plug the numbers into the formula, we should simplify the formula and change the signs.

Simplify the mass--we can do this because the mass of the first car is identical to the mass of the second car: m1 = m2 = m.

Simplify the final velocity--we can do this because the two cars will bump into each other. When two bodies collide and start moving together, the collision is called an inelastic collision. In inelastic collision the final velocities of the two bodies are the same: vf1 = vf2 = vf.

Now our formula for an inelastic collision after the simplification looks like

Change the signs--we must do this because in this problem we are dealing with momentum which is a vector quantity. Since the two cars are moving toward each other, which means they are moving in opposite directions, it is up to us which direction we choose to be positive or negative. Usually in physics the right direction is positive and left is negative.

   vi1=15m/s (positive)
   vi2= -10m/s (negative)

Now we can plug in all the numbers

m X 15 m/s + m X (-10 m/s) = (m + m) X vf

15m -10m= 2mvf

To find the final velocity, cancel the mass (m) on both sides of the equation to get

15 - 10 = 2vf
5 = 2vf

To get vf divide both sides of the equation by 2

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Question: What is the final velocity of the cars?

Type your answer here: m/s