Integral for displacement from velocity

AI Thread Summary
The discussion revolves around calculating the displacement of an object using its velocity equation, v(t) = [(3/2)(m/s²)t] i^ + [(3/2)(m/s³)t²] j^. The user initially struggles with the integration process and arrives at an incorrect displacement magnitude. After some back-and-forth, it is clarified that the correct components of the displacement vector are 3 and 4, leading to a final displacement magnitude of 5. The confusion stemmed from arithmetic errors rather than the integration method itself. The conversation highlights the importance of careful calculations in vector magnitude determination.
burton95
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Homework Statement


An object is moving with a velocity by the equation

v(t) = [(3/2)(m/s2)t] i^ + [(3/2)(m/s3)t2] j^

What is the magnitude of displacement during 0 - 2s

Homework Equations



v(t) = [(3/2)(m/s2)t] i^ + [(3/2)(m/s3)t2] j^

The Attempt at a Solution



(3/2) ∫ from 0 to 2 [(t2 / 2) i^] + [t3/3]y^

plug and chug with t = 2

(3/2) √(squaring each of the i^ + j^)

I end up with some decimal answer which I know is wrong. Where am I screwing up?
 
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Who says you're wrong. What do you get? Is it something like 6.5?
 
When I plug in 6.5 to the online quiz it says sorry wrong answer, "Don't forget to add the components of a vector quadratically to determine it's magnitude." I don't understand where I'm going wrong. Help
 
Last edited:
wait what about the units of s^2 and s^3?

EDIT: I don't think that's it
 
Last edited:
Oops. 6.5 was wrong. I must have made a mistake somewhere. Here are the correct results: What did you get for the two components of the displacement vector? I got 3 and 4 using your equation. They were 3/2 x 2, and 3/2 x 8/3. So the correct displacement magnitude must be 5.

Sorry for any confusion I caused. It looks like you had it right all the way, but just made a mistake in arithmetic.

Chet
 

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