Help me understand how to solve this and other vector problems

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Feramushna
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$10.00 Help me understand how to solve this and other vector problems

From Mathematics: Linear-Systems
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Due on Nov. 23, 2008
Asked on Nov 18, 2008 at 4:06:30PM

Q:
a) A particle travels in space along the path r(t) =
2ti + 3t^2 j + (sin t)e^-t K metres, where variable t denotes time, in seconds. Find it's velocity and acceleration.

b) Find the curvature, at the point with parameter t, of the (elliptic) plane curve r(t) = 2sin t i + 3 cos k

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sudipta

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Posted on Nov 18, 2008 at 5:24:45PM

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Preview: ... city vector v(t), we take the derivative of r(t) with respect to t, as shown: v(t) = d r(t) / dt = d(2t)/dt i + d(3t^2)/dt j + d[(sin t)e^(-t)]/dt k = 2i + 6t j + (cos t - sin t)e^(-t) k To find the acceleration vector a(t), we take the d ...

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Xcel
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Posted on Nov 18, 2008 at 5:49:41PM

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Preview: ... 3cost k r'xr''= i j k 2cost 0 -3sint -2sint 0 -3cost =oi-(-6(cost)^2-6(sint)^2)j+ok = 6((cost)^2+(sint)^2)j = 6j abs(r'xr'')= sqrt(6^2) = 6 abs(r')= sqrt( (2cost)^2+(-3sint)^2 ...

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bibhupada
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Posted on Nov. 19, 2008 at 12:58:25AM

A:
Preview: ... is the rate of change of path with respect to time t so d/dt(r(t))=d/dt(2ti+3t^2j+(sint)e^(-t)k) dr/dt=2i+6tj+(coste^(-t)-sint e^(-t))k,which is the velocity rate of change of velocity is the ac ...

The full tutorial is about 115 words long .