Volumes of Solids

Method: Physics Relationships

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, v ( 0 ) = 300 mi 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 a ( t ) = 16 ft s 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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