- #1

QuarkCharmer

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## Homework Statement

A particle is moving with the given data. Find the position of the particle.

[itex]a(t)=t^{2}-4t+6[/itex],

[itex]s(0)=0[/itex],

[itex]s(1)=20[/itex]

## Homework Equations

## The Attempt at a Solution

[itex]a(t)=t^{2}-4t+6[/itex], [itex]s(0)=0[/itex], [itex]s(1)=20[/itex]

[tex]v(t)=\int t^{2}-4t+6 dt[/tex]

[tex]v(t)=\frac{t^{3}}{3}-2t^{2}+6t+C_{1}[/tex]

Then I suppose I take the antiderivative again to get to s (distance), I can't solve for the constant yet.

[tex]s(t)=\int \frac{t^{3}}{3}-2t^{2}+6t+C_{1} dt[/tex]

[tex]s(t)=\frac{t^{4}}{12}-\frac{2t^{3}}{3}+3t^{2}+C_{1}t+C_{2}[/tex]

So now I have two constants in there? Would I just use the parameters [itex]s(0)=0[/itex] and [itex]s(1)=20[/itex] to try to solve this like a system of 2 equations with two unknowns? I don't really know how to proceed. The other problems like this at least gave me a value for the first derivative of the original function so I could sort of work backwards.

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