(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Particle trajectories

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