# Curves on a Plane

#### Jason76

We are given the position of the particle at time t.

(a) Find an equation in x and y whose graph is path of the particle.

(b) Find the particle's velocity vector at the given value of t.

(a)

$$\displaystyle x^{2} - 2x$$ - ??

(b)

$$\displaystyle r(t) = (t + 1)i + (t^{2} - 1)j$$

$$\displaystyle t = 1$$

$$\displaystyle v = (t)i + (2t)j,$$

$$\displaystyle v(1) = (1)i + (2(1))j,$$

$$\displaystyle i + 2j$$ - velocity vector at given value of t

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#### GLaw

For (a) you are supposed to eliminate $t$ from the parametric equations $x=t+1,\,y=t^2-1$ to obtain an equation in just $x$ and $y$. Your answer should involve $y$ as well, not just $x$.

In (b), if the given value of time is $t=1$, that it’s correct.

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