How do I go about this? I finished it but I think its off a bit. I think it has to do with the extra constant that comes out of integration that I didn't take into account.(adsbygoogle = window.adsbygoogle || []).push({});

Problem: The position of a particle at times t=10 sec and t=5 sec are known to be, respectively,

[tex]\vec{r}(10) = 10\vec{i}+5\vec{j}-10\vec{k}[/tex]

[tex]\vec{r} (5) = 3\vec{i}+2\vec{j}+5\vec{k}[/tex]

What is the acceleration of the particle at time t=5 sec if the velocity vector has the form

[tex]\vec{v}=C_1\vec{i}+C_2 t^2\vec{j}+C_3\ln{t}\vec{k}[/tex]

where C_1, C_2, and C_3 are constants and t is time in seconds?

What I did:

integrated v(t) to get r(t), [itex]\vec{r}(t)=C_1 t\vec{i}+\frac{1}{3}C_2 t^3\vec{j}+C_3(t\ln{t}-t)\vec{k}[/itex] then integrated once more to get a(t)= [itex]2C_2 t\vec{j} +\frac{C_3}{t}\vec{k}[/itex]

I then substituted the initial equation for r(5) into the equation for r(t) to find the constants C_1, C_2, C_3, and then using these constants, found the acceleration for t=5 to be [itex].48\vec{j}+.33\vec{k}[/itex]

The values I got for the constants were .6 for C_1, 6/125 for C_2, and 1/(ln(1)-1) for C_3.

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# Particle acceleration

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