Volumes of Solids

Identifier: Distance vs. Displacement

The identifiers for this type of problem are usually very straightforward.

They will start you with a velocity equation, v(t) , and then they will ask you questions about different types of positions .

Many students are thrown when they get a velocity equation because they don’t know how a velocity can provide them information about their position. Recall that when you use antiderivatives as an accumulation tool that what you are accumulating is the units of what is “on top”, the dy units. If your velocity equation, v(t) , is in terms of m s = meters second , then taking the antiderivative of velocity, v(t) , will give us the Net meters , over a given time interval, [ a , b ].

They will often flat out ask you to find the “ displacement ” or your “ total distance traveled”. They can also use language that implies one or the other, and when they do you want to look out for that word “ total ” it is normally used when they want the “ total distance traveled”.

How from you’re the starting location are you? This would be displacement.

How far was your total trip? This would be total distance.

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