Vector jerk is the 3 derivative?

[XwakeriderX]

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?

 

[PhanthomJay]

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?? 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?

 

[XwakeriderX]

i was!
So i can't 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 I am lost so is the answer 74 m/s^3 orrr

sqrt(74 + 0)

 

[PhanthomJay]

i was!
So i can't 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 I am 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?

 

[XwakeriderX]

Hmm so the final answer "in unit vector form" is 74y_^ m/s^3

I'd say I am decent :P havnt taken stats though but i do believe in getting lucky!

 

[PhanthomJay]

Hmm so the final answer "in unit vector form" is 74y_^ m/s^3

I'd say I am 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.

 

[XwakeriderX]

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=_____75_y__________ m/s³

 

[PhanthomJay]

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.

 

[XwakeriderX]

Yeah its 75y_hat, that's 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!