Physics

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In short, momentum is vector and kinetic energy is scalar.

$\begin{matrix} (1) & \vec{p} = m \vec{v} \end{matrix}$ $\begin{matrix} (2) & T = \frac{1}{2} m {\vec{v}}^{2} = \frac{\vec{p}}{2 m} \end{matrix}$

Two momenta in opposite direction is $0$ . Total energy and momentum both are conserved, let total energy =kinetic energy + potential energy. Here kinetic energy changes its form (it mostly converts to other energy since energy can never be destroyed) while momentum is conserved body to body. In equation (2) I had shown that kinetic energy is mostly relevant to momentum (but they aren't same), the core difference here is one is scalar another is vector. Let's look at their units (other prefers dimension but I like units), units of momentum is $k g m$ while units of kinetic energy is $k g m^{2}$ . Kinetic energy is movement energy of an object. Think that, in a system some kind energy is converted to kinetic energy, so the energy will make particles move in that system.

If two objects move at the same speed then the more massive one has more quantity of motion and if two objects have same mass then the faster one has more quantity of motion.

Kinetic energy is energy of moving object.

An integral form might be more helpful to understand the difference,

$\vec{p} = \int \vec{F} dt$ $W = T = \int \vec{F} \cdot d \vec{s}$

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Thanks, and I'm sure that makes it intuitive to a physicist, but it's not quite what I was hoping for... (1 comment)

This answer doesn't address the question. (1 comment)

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How can the kinetic energy equation be intuitively understood?

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