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The motion of two cars is described by the following position vectors:

$$\vec {r}_1 = t \space (9 - t) \cdot \vec {i} + (t^2 - 10 \space t + 9) \cdot \vec {j}$$

and

$$\vec {r}_2 = (2 \space t^2 - 19 \space t + 9) \cdot \vec {i} + 2 \space t \space (t - 9) \cdot\vec {j}$$

...where $\vec {i}$ and $\vec {j}$ are the unit vectors in the $xy$ plane and $t$ is time. All the units are SI.

What are the magnitudes of the cars' velocities just before they collide?

A

$v_1 = 12 \space m/s$
$v_2 = 25 \space m/s$

B

$v_1 = 25 \space m/s$
$v_2 = 12 \space m/s$

C

$v_1 = 0 \space m/s$
$v_2 = 0 \space m/s$

D

$v_1 = 8 \space m/s$
$v_2 = 5 \space m/s$

E

$v_1 = 5 \space m/s$
$v_2 = 8 \space m/s$

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