Vector jerk is the 3 derivative?

  • #1

Homework Statement


r(t)=(5.00t2x + 12.5t3y meters
The position r of a 12.0 kg mass, moving in the x-y plane




Homework Equations


Third derivative....
sqrt(x2+y2)


The Attempt at a Solution


Is it correct to just take the third derivative and plug in 12 kg and find the magnitude and that would be a jerk?
 

Answers and Replies

  • #2
PhanthomJay
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X*.*X: No.
Now first off, those x and y variables are actually x_hat and y_hat unit vectors (usually denoted as i and j unit vectors). It means the position of the mass is at any time t is 5t^2 meters in the x direction and 12.5t^3 meters in the y direction. Were you not paying attention last time in your very first post to this forum??:wink: The third derivative is the rate of change with acceleration with respect to time (affectionately called a jerk). What's mass got to do with it?
 
  • #3
i was!
So i cant do this?!
r(t)=(5.00t^2x + 12.5t^3y)dt

r(t)=10t +37t^2 --> velocity m/s 1st derivative

r(t)=10 +74t ---> Acceleration m/s^2 2nd derivative

r(t)=74 ----> Jerk m/s^3

okay ha now im lost so is the answer 74 m/s^3 orrr

sqrt(74 + 0)
 
  • #4
PhanthomJay
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i was!
So i cant do this?!
r(t)=(5.00t^2x + 12.5t^3y)
note my correction, where the bold letters represent unit vectors
r'(t)=10tx +37t^2y --> velocity m/s 1st derivative
yes, and note bold unit vectors
r''(t)=10x +74ty ---> Acceleration m/s^2 2nd derivative
yes
r'''(t)=74 y----> Jerk m/s^3
, yes, in what direction??
okay ha now im lost so is the answer 74 m/s^3 orrr

sqrt(74 + 0)
Scratch that last answer, please. Say, if the Sox beat the Yanks 6 straight, we got a chance! Are you any good at Probabilities?
 
  • #5
Hmm so the final answer "in unit vector form" is 74y_^ m/s^3

I'd say im decent :P havnt taken stats though but i do believe in getting lucky!
 
  • #6
PhanthomJay
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Hmm so the final answer "in unit vector form" is 74y_^ m/s^3

I'd say im decent :P havnt taken stats though but i do believe in getting lucky!
Yes correct! And now I see what you were trying to do with that square root thing, using Pythagorus as your guide...but its jerk = square root of (0^2 + 74^2), or jerk = 74m/s^3 in y direction, same result!
Excellent, my friend!

edit: oops, math error, 12.5 x 3 =37.5, so the answer for jerk magnitide is 75, not 74, no biggy.
 
Last edited:
  • #7
ah yeah i was rushing :p Thanks again! Still trying to figure out how to actually write down my answer

Answer box is given J=_______________ m/s3

J=_____75y__________ m/s3
 
  • #8
PhanthomJay
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Since J is in the y direction, you'd have to give the answer in unit vector form, J =75y_hat....I don't know how the answer box handles vector notation....probably in the same way x and y was noted in the original equation for r.
 
  • #9
Yeah its 75y_hat, thats how things are displayed in my notes! awesome once again you save the day! Now on to 2 blocks 1 pulley on an incline problem! ha this should only take me a few hours!
 

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