Kinematic Equations

Kinematics is essentially the field of mechanics that describes how objects move without directly discussing the forces that they interact with. This is suitable, especially for people who haven't been introduced to forces before.

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The following equations can be used to solve for the quantities within them. They can also be applied to freefall and projectile using angled quantities.



Kinematic Equations

The five equations(labeled) above are the main 5 kinematic equations. Note that all of these equations assume the object/system they apply to is undergoing constant acceleration(unchanging). All 5 of the equations can be used in both the x and y directions. In fact, to analyze freefall motion and projectiles, you'll need to likely apply these equations in both directions.

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In Equation 1, the displacement is omitted so use this if you don't know the displacement but want to solve for another quantity.

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In Equation 2, the time is omitted so use this if you don't know the time but want to solve for another quantity.

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In Equation 3, the final velocity is omitted so use this if you don't know the time but want to solve for another quantity.

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In Equation 4, the initial velocity is omitted so use this if you don't know the final velocity but want to solve for another quantity.

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In Equation 5, the acceleration is omitted so use this if you don't know the acceleration but want to solve for another quantity.


If you deal with these equations in multiple dimensions/at angles, you can set up right triangles to find the components of velocity, acceleration, or position vectors in whatever dimension you want. If angles are given to find these, you'd have to use sine, cosine, or tangent to find the components of vectors. If angles aren't given but the components of vectors are, then the Pythagorean Theorem is available to use.


Citations/Attributions