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Aaron was biking due east but had to stop for a light. Just as the light turned green and Aaron began to accelerate at a constant rate his friend Betty sped by on her bike traveling in the same direction with constant velocity $V$.

If it took Aaron time $T$ to accelerate to Betty's speed, how long did it take him to catch up to Betty?

A

$T$

B

$\sqrt { 2 }T$

C

$2T$

D

$4T$

E

$\frac { 1 }{ 2 } { T }^{ 2 }$

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