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.