The Equations of Motion

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The three major variables that we use in studying motion are displacement (distance), velocity (speed) and acceleration. We could also include a fourth variable, time, since this variable is included in most of the equations that we use.

These variables can be combined into three basic equations:







acceleration equation



We can do a lot with these equations, however, they have limitations. By themselves, we can use these equations to solve simple problems. To solve more complex problems, we must combine these equations together to create new, larger equations. If the acceleration of an object varies, however, the motion will be too complex for these new, combined equations. So these new equations will only work when the acceleration is constant.

There are four variations to combining these equations. These four new equations are often called the equations of motion or the kinematics equations. Again, these kinematics equations may be used to solve any motion problem where acceleration is constant.


 First Equation of Motion

First Eq Of Motion


Second Equation of Motion

2nd eq


Third Equation of Motionthird eq


Fourth Equation of Motion

4th eq


These equations are meant to be used as a group. Usually you will only need to use one of these equations to solve a problem. Sometimes, however, you will need to use two of them to solve a problem. The key to solving a kinematics problem is to use the equation where you have three known variables and only one unknown variable.


How do you use the kinematics equations to solve a

physics problem?



Just so you know, there are other ways that we could write them. For example,

Displacement can be rewritten as,

Displacement only

And if we substitute this expression into the second equation of motion we get,

eq change 1

We can rearrange this equation even further to solve just for the final position of an object (xf). Do solve for final position we can move xi to the other side of the equals sign by adding xi to both sides of the equation.

eq change 2

And finally, we end up with an expression that can solve for the final position of an object,

eq change 3

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