Can someone help me with an analytical dynamics exercise?

[Doney Felipe MEjia]

At a certain instant, the velocity and acceleration of a particle ar defined by v= 3i + 4j - 6k m/s and a=-2i + 3k m/s2. Find the radius of curvature and change of speed of the particle at the instant.

 

[Henryk]

change of speed of the particle at the instant

you mean, the rate of change of speed, that is acceleration parallel to the trajectory, right?
I also assume, that i, j, k refer to unit vectors along x, y, z coordinates, respectively.
This is not a hard thing to do. First, you have to construct a unit vector parallel to the velocity vector ## \hat v =\frac{ \vec v }{]v]} ##.
The parallel acceleration is just a projection of the acceleration onto direction of ## \hat v ## , that is ## a_{\parallel} = \hat v * (\hat v \cdot \vec a) ##
That will give you the answer to the second of your question.
The curvature can be found from the formula ## \frac {v^2} r = a_{\perp} ## where ## a_{\perp} = \vec a - a_{\parallel} ##

I hope that I gave you enough hints. If you have any more questions, let me know.
H

 

[Doney Felipe MEjia]

oh man, thank you so much! It's really easy to do now, but I was confused about it! I have another question from the other exercise but I want to keep trying solve this exercise. if I don't get to solve it, I'll request your help again. Thanks H.

 

[berkeman]

oh man, thank you so much! It's really easy to do now, but I was confused about it! I have another question from the other exercise but I want to keep trying solve this exercise. if I don't get to solve it, I'll request your help again. Thanks H.

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