- Figure out what you are trying to find, and write down the variable that represents it.
- Figure out what things you have. Write down their values - both variable name, number and units, in the format "
`v`". How to identify what variables you have in a problem is discussed in more depth below._{i}= 4 m / s - Convert all the things you have into units that involve kg, m, and s. I should see the conversion process written out on your paper. These units are the standard building blocks for all units in physics; the equations we use assume that you have units made up of these. Thus, you need to get rid of things like cm, g, or h. This is why we studied factor-label conversion first. As a review, here are the conversion equations you need to know:

1000 m = 1 km 60 s = 1 min 1000 g = 1 kg

1000 mm = 1 m 60 min = 1 h

100 cm = 1 m

10 mm = 1 cm - Now you are ready to approach the problem; you've laid out all the pieces, and you need to figure out how to put them together. Being prepared like this before I start looking for an equation gives me a confident feeling about the problem, sort of like when you're doing a jigsaw puzzle and you go through the box first and pull out all the edge pieces, or all the pieces with blue on them. You have a manageable number of variables to worry about, and you have them all together in one place.

Now we want to find an equation that will give us the thing we want, using what we have. You won't always be lucky enough to get an equation with your wanted variable on one side and all the others clustered on the other side. However, any time that you know all the variables in an equation except the one you want, you can solve for that variable using algebra.

So, you want to look through your list of equations and find one that includes the variable you want, and for which all the other variables are known. The table below gives a list of equations you might need, and what variables are involved in them (I find that this list makes it easier to quickly see which ones I can use). The uses of these equations are described in more detail in section 2 below.Equation Variables

v_{avg}= (Δx)/(Δt)v _{avg}, Δx, Δtv _{avg}= (x_{f}- x_{i})/(t_{f}- t_{i})v _{avg}, x_{f}, x_{i}, t_{f}, t_{i}a = (Δv)/(Δt) a, Δv, Δt v _{f}= v_{i}+ aΔta, v _{f}, v_{i}, ΔtΔx = .5(v _{f}+ v_{i})ΔtΔx, v _{f}, v_{i}, ΔtΔx = v _{i}Δt + .5a(Δt)^{2}Δx, Δt, a, v _{i} - Plug your numbers into that equation. I find that it's easier just to work with bare numbers in solving the equation, since plugging the units in as well gets me confused; however, it's more professional to put the units in
- Finally, you want to solve your equation using algebra.

In free fall problems, we often talk about the height of something above the ground. This is also a position. Here, x increases as you go up and decreases as you go down.

You should be aware that all these x's can be positive or negative. If the height or position of some object decreases during the time the problem is concerned with, then the Δx is negative. So, it's not simply an answer to "how far;" it also tells you how far

Examples:

A ball was thrown from a height of 2.8 m to a height of 4.5 m. | These measurements are in m, so they are x's of some sort. The problem uses from and to, and definite starting and ending positions are given relative to something else (the ground). So, x_{i} = 2.8 m and x_{f} = 4.5 m. |

How far does the car go? | Here, the question is a "how far." We don't care where it was at the start and end, just the distance traveled in between. So, it is a Δx. |

Time is always measured in something like seconds, hours, or minutes. The standard units for time are seconds.

Velocity cannot be measured directly. It can only be measured by observing how far an object moves in a known time interval, and dividing.

There are four different types of velocities that you should be aware of. When an object is moving at a more or less constant pace, we say that it is moving at some

When objects are accelerating, their velocity is changing. In this situation, we start to have to deal with three more types of velocity: initial velocity, final velocity, and change in velocity. v

The final thing you need to know about velocity is that one particular velocity, 0 m / s, has a lot of other sneaky names. This is the velocity that means that an object's position is not changing as time goes on - it is the velocity of an unmoving object. We might also say that the object is "at rest," or "still." If an object is "released" at the start of its motion, or if it "stops" at the end of its motion, this means that the start or end velocity, respectively, is zero.

Examples:

A car going 2 m / s stops. | The 2 m / s is clearly a velocity, by its units. To figure out what velocity it was, I might try to explain the situation with different words: "A car was going at 2 m / s and then it stopped." Now it's clear that v_{i} = 2 m / s. The problem also tells us that the car stopped. "Stop" means a velocity of 0 m / s, and it is clearly at the end of the motion, so v_{f} = 0 m / s. |

The car sped up by 4 m / s. | This deals with a change in the velocity of the car. The original velocity could be 0 m / s or 120 m / s, for all we know. So, all we have is Δv = +4 m / s. Actually, if the car is going backwards, we might have Δv = -4 m / s; all we know is that it "sped up." |

The one tricky thing here is in free fall problems, where the acceleration is given to you for free. Any accelerating object has an acceleartion of g = -9.8 m / s

These two equations are the ones that you will find yourself using most in acceleration problems. They tell you how to find the distance that an objects travels, while accelerating, in a given time. One uses the beginning and ending velocities, one uses just the starting velocity and the acceleration.

Solving the equation may be the hardest part for some of you. Here are some tips on algebra techniques you may find useful:

Remember, I won't take many points off for algebra mistakes. The physics part of the problem is the part that takes you from a description of a situation into an algebraic equation. However, you do need to know algebra to do well in this class. If you see one of the situations above, it should leap off the page and tell you that it's time to use one of these tricks.