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Particle trajectories 
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#1
Nov1612, 01:34 PM

P: 783

1. The problem statement, all variables and given/known data
At time t = 0, a particle is located at the point (1, 2, 3). It travels in a straight line to the point (4, 1,4), has speed 2 at (1, 2, 3) and constant acceleration 3i  j + k. Find an equation for the position vector r(t) of the particle at time t. 2. Relevant equations 3. The attempt at a solution If we integrate the acceleration vector twice, we get the position vector (along with some constants we must determine). Plugging in the initial position vector gives us [tex] r(t) = <1.5t^{2},.5t^{2},.5t^{2}> + v_{0}t + <1,2,3>[/tex] The problem is I don't know how to find the initial velocity. That's all I need to complete the problem. I know the speed at time t=0, but not the velocity. I also know that the particle travels in a straight line, meaning its unit tangent vector is constant and that its motion is nonperiodic, but how does that help? BiP 


#2
Nov1612, 03:30 PM

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#3
Nov1612, 03:34 PM

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#4
Nov1612, 11:26 PM

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Particle trajectories
BiP 


#5
Nov1712, 12:05 AM

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#6
Nov1712, 04:22 PM

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