# Is kinetic energy directly proportional to momentum?

Kinetic energy is to do with an object's mass and velocity, so is momentum. Are these basically the same thing?

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I wouldn't say so. Momentum is proportional to the mass and speed. Kinetic energy is proportional to the mass and < speed squared >. This makes the relationship between Momentum and Kinetic energy kind of strange. If you increase only the mass, then Kinetic Energy and Momentum will be directly proportional, but if you increase the speed, Kinetic Energy and Momentum will not have a directly proportional relationship. The trick is that both Kinetic Energy and Momentum depend on 2 variables, mass and speed.

It's also important to note that Linear Momentum is also a vector quantity, though its magnitude can be considered a scalar. Kinetic Energy, on the other hand is always a scalar. I think this really makes the two concepts very different and you have to be precise about when and why you compare the two. Linear Momentum is a concept that describes an object's motion. Kinetic Energy describes an object's "stored energy" in the form of motion, energy meaning its ability to do work on other objects.

• Kinetic energy (KE) = 0.5 mv^2

However, momentum = mv so, we can write

KE = 0.5 v x momentum

For y to be proportional to z: (y =kz) , then k must be a constant.

However, the 0.5v is not a constant as v varies; momentum is also a function of v

So, in my opinion KE is not direct proportional to momentum.

• Anonymous
8 years ago

kinetic energy is 1/2 mass * (velocity)^2

momentum = mass * velocity

so kinetic = momentum^2 / mass*2

• another formula for momentum is

p = Ek/c

thus, yes they are directly porportional, but they are NOT equal to the same thing.