Carts a and B Have Equal Masses and Travel Equal $\overrightarrow{\mathbf{v}}$

Multiple Choice

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities $\overrightarrow{\mathbf{v}}$ A and $\overrightarrow{\mathbf{v}}$ B of the bodies at the end of distance D are related by:

A) $\overrightarrow{\mathbf{v}}$ B = $\overrightarrow{\mathbf{v}}$ A .
B) $\overrightarrow{\mathbf{v}}$ B = $\sqrt{2}$
$\overrightarrow{\mathbf{v}}$ A.
C) $\overrightarrow{\mathbf{v}}$ B = 2 $\overrightarrow{\mathbf{v}}$ A.
D) $\overrightarrow{\mathbf{v}}$ B = 4 $\overrightarrow{\mathbf{v}}$ A.
E) $\overrightarrow{\mathbf{v}}$ A = 2 $\overrightarrow{\mathbf{v}}$ B.