The method for these physics problems are going to be the same methods you learned for solving an Initial Value Indefinite Integral problem. The only difference is that these problems have some “real-world” meaning.

**
Step 1:
**Identify all your given data in terms of the physics relationships *
position
**
,
**
s(t)
**
,
**
velocity
**
,
**
v(t)
**
, and
**
acceleration
**
,
**
a(t)
**
.
*

These problems don’t always just hand you the given information about *
position
*, *
velocity
*, and *
acceleration
* that you might need.

Sometimes you will need to read through the language of the problem keeping in mind the *
physics
* ideas of *
position
*, *
velocity
*, and *
acceleration
*.

They might say, “Blah *
started
* on the top of a *
30-foot-high
*tower.” Well, this is them subtly providing you the *
initial
*position, *
s(0)=30ft
*. Or they say, “The rocket ship is *
initially
* moving at a *
speed
* of *
300 miles per hour
*.” That is there way of letting you know the *
initial
*velocity, $\textcolor[rgb]{}{v}\textcolor[rgb]{}{\left(}\textcolor[rgb]{}{0}\textcolor[rgb]{}{\right)}\textcolor[rgb]{}{=}\textcolor[rgb]{}{300}\frac{\textcolor[rgb]{}{\mathit{mi}}}{\textcolor[rgb]{}{\mathit{hr}}}$. They might say something like, “The *
acceleration
* due to gravity was *
16 feet per second squared
*.” From that you would need to know that the complete acceleration equation is $\textcolor[rgb]{}{a}\textcolor[rgb]{}{\left(}\textcolor[rgb]{}{t}\textcolor[rgb]{}{\right)}=\textcolor[rgb]{}{\u2013}\textcolor[rgb]{}{16}\frac{\textcolor[rgb]{}{\mathit{ft}}}{{\textcolor[rgb]{}{s}}^{\textcolor[rgb]{}{2}}}$ because gravity is a constant. (*
Notice
* the *
negative sign
*, they love to not talk about gravity as a *
negative
*acceleration, but remember it always is.)

Additionally, you want to be very careful with the units in these problems as some unit conversion might need to take place. If your *
velocity
*is in *
miles
**
per hour
*, and your position is talking *
feet
*, you will need to convert the units of one to the other based upon the *
units that the final answer requires
*.

**
Step 2:
**Setup and apply the Initial Value Indefinite Integral process.

Usually, you will start with an acceleration equation, which may only a constant value. Remember *
gravity
* is a *
constant
*amount of acceleration.

Depending on your specific problem, you will either run the Initial Value Indefinite Integral process *
once
* to get back to the *
velocity
*equation, *
v(t)
*.

Or you will then run the Initial Value Indefinite Integral process a*
second time
* to go from the *
velocity
*equation, *
v(t)
*, back to the original *
position
*equation, *
s(t)
*.

**
Step 3:
**Answer the actual question.

Often times in these problems you will want you to find the position *
equation
* not just for the sake of getting back to the position *
equation
*, but to actually answer a question that is related to the position of an object.

For example, you might be asked about when something would hit the ground, or would you run into that wall?

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