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I'd like to say that solving numerical kinematics problems is highly creative problem solving at its best  but that would be a lie. Although beginning physicists often find kinematics problems quite challenging at first, once you get the idea, they are generally pretty routine.
In order to get into the rhythm of solving kinematics problems as quickly and easily as possible, use the following steps to guide your problemsolving efforts. This method is illustrated in several examples on the following pages.
Remember that there will be many situations in physics in which your solution to a problem will be graded  not just the answer. In fact, in many cases, the solution will be weighted much more heavily than the correct answer. Therefore, it is important to develop a professional problemsolving style. Here's a good way:
In order to apply the power of mathematics to kinematics problems, you need to be able to translate a verbal description of a kinematics problem into the symbolic language of mathematics.
A kinematics problem generally consists of three situations. In the original (or starting) situation, some object is located at position "x_{o}" and has velocity "v_{o}" at the instant that the clock reads "t_{o}". Then, the object has a constant acceleration "a" for some time "" while it moves a distance "". In the final situation, the object is located at position "x" and has velocity "v" at the instant that the clock reads "t". Given values for some of these quantities, your job is to find values for some of the others.
The table below shows the variables that we will use to represent each kinematics quantity.
Customary Symbols for Kinematics Quantities 


Kinematics Quantity 
Mathematical Symbol 
Position: 

final position  where the object is located at the instant the clock reads "t" 

original (or starting) position  where the object was at the instant the clock read "t_{o}" 

displacement (signed, net) distance the object moved 

Velocity: 

final velocity  the object's speedometer reading at the instant the clock reads "t" 

original (or starting) velocity  the object's speedometer reading at the instant the clock reads "t_{o}" 

change in velocity 

average velocity 

Acceleration: 

(constant) acceleration 

Time: 

final clock reading 

original (or starting) clock reading 

time interval (change in time) 

In the table below, you will find the 7 equations that you need to know to solve kinematics problems. Don't panic! The first 3 equations are definitions that you have already seen! Notice that the equations in the table have been divided into two groups. The "green group" are mostly kinematics definitions. Using these equations often leads to multistep solutions of kinematics problems  but each step is pretty simple. The "blue group" are more sophisticated equations that can often solve kinematics problems in one step, but the algebra involved in using them is often slightly more complicated. The following pages will show you where these equations come from, and show how the equations can be used to solve kinematics problems.
The Equations You Need to Know to Solve Kinematics Problems (Memorize These Equations) 


Kinematics Equation 
Comment 

The definition of displacement in algebraic symbols Note that "" always means "change in", and anything always means "final value  original value". Therefore, defines "change in velocity" and defines "change in time". 

This is the definition of average velocity in mathematical symbols. (A bar over a quantity denotes "average".) Velocity is the rate position changes. Average velocity is displacement divided by time. This equation is often seen in the form , which says, essentially, "distance equals average velocity times time" 

This is the definition of acceleration in mathematical symbols. Actually, we said that average acceleration is change in velocity divided by time, but since acceleration is constant, average acceleration and instantaneous acceleration are the same. Here are some examples of its use in solving kinematics problems. 

This equation says that if the acceleration is constant, the average velocity in any time interval is simply the average of the original and final velocities. It is very simple to use and handy in simplifying many calculations. Its derivation requires calculus, though. 

This equation is the good old "distance equals average velocity times time" you learned back in 5th grade  dressed up a bit! It can be very useful, particularly in conjunction with the previous equation. 

This equation is very closely related to , and often either one can be used to solve a problem. Click here to see how this equation is used, and where it comes from. 

This equation is useful in many situations. Here are some examples, and here is its derivation. 

In many kinematics situations, you know speedometer readings, acceleration, and distance, but you don't know the time interval involved. This equation comes to the rescue in this situation. Here are some examples. 
BHS > Staff > Mr. Stanbrough > Physics > Mechanics > Kinematics > this page