Integral for displacement from velocity

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Homework Help Overview

The problem involves calculating the displacement of an object given its velocity as a function of time, expressed in vector form. The specific time interval under consideration is from 0 to 2 seconds.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the integration of the velocity function to find displacement and raise questions about the correctness of their calculations. There is also a focus on the proper method for determining the magnitude of the displacement vector.

Discussion Status

Some participants have provided feedback on the calculations, questioning the arithmetic and suggesting that the original poster may have made a mistake. There is an ongoing exploration of the components of the displacement vector and how to correctly calculate its magnitude.

Contextual Notes

Participants are considering the implications of the units involved in the velocity equation and how they affect the calculations. There is also mention of an online quiz that provides feedback on the answers submitted.

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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