Find the antiderivative of the following vector:

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Homework Statement


Calculate the position vector of a particle moving with velocity given by:

v = (32 m/s - (5 m/s^2 )t i) + (0 j)

Homework Equations



(x^(n+1) / (n+1) ) + C = antiderivative of function

The Attempt at a Solution



r = (32t m - (5/2)t^2 m/s + C m i) + (C j)

Honestly, I'm just confused with the units more than anything. I don't know why the problem has m/s^2 if it's a velocity vector...
 

Answers and Replies

  • #2
SteamKing
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Homework Statement


Calculate the position vector of a particle moving with velocity given by:

v = (32 m/s - (5 m/s^2 )t i) + (0 j)

Homework Equations



(x^(n+1) / (n+1) ) + C = antiderivative of function

The Attempt at a Solution



r = (32t m - (5/2)t^2 m/s + C m i) + (C j)

Honestly, I'm just confused with the units more than anything. I don't know why the problem has m/s^2 if it's a velocity vector...

A quantity of 5 m/s2 indicates that accelerated motion is taking place, i.e., the velocity is changing w.r.t. time. Acceleration × time = change in velocity.
 
  • #3
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A quantity of 5 m/s2 indicates that accelerated motion is taking place, i.e., the velocity is changing w.r.t. time. Acceleration × time = change in velocity.

oooooh okay that makes more sense. thank you!

and the antiderivative is right, right?
 
  • #4
SteamKing
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oooooh okay that makes more sense. thank you!

and the antiderivative is right, right?
I would say that since the velocity vector had no j-component, the position vector will not either.
 
  • #5
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I would say that since the velocity vector had no j-component, the position vector will not either.
but isn't the antiderivative of 0 C (or in this case, D to differentiate)?
 
  • #6
SteamKing
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but isn't the antiderivative of 0 C (or in this case, D to differentiate)?
Yeah, but D = 0 would be an acceptable value for the constant of integration, in the absence of any other initial condition information.
 
  • #7
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Yeah, but D = 0 would be an acceptable value for the constant of integration, in the absence of any other initial condition information.

oh okay. since this is on a take home test, do you think I should just put both answers (one for a definite integral 0 and one for an indefinite integral D)?
 
  • #8
SteamKing
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oh okay. since this is on a take home test, do you think I should just put both answers (one for a definite integral 0 and one for an indefinite integral D)?
You can have a definite integral only if you know the value of t.
 
  • #9
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You can have a definite integral only if you know the value of t.

hmm... so what should I put down?
 

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