Spike Claims That Dimensional Analysis Shows That the Correct Expression $\vec { v } _ { f } - \vec { v } _ { i }$

Multiple Choice

Spike claims that dimensional analysis shows that the correct expression for change in velocity, $\vec { v } _ { f } - \vec { v } _ { i }$ ,is $\vec { v } _ { f } - \vec { v } _ { i } = \frac { m t } { F }$ ,where m is mass,t is time,and F is the magnitude of force.Carla says that can't be true because the dimensions of force are $\left[ \frac { \mathrm { ML } } { \mathrm { T } ^ { 2 } } \right]$ .Which one,if either,is correct?

A) Spike,because $[ \vec { v } ] = \left[ \frac { M L } { T } \right]$ .
B) Spike,because $[ \vec { v } ] = \left[ \frac { T ^ { 2 } } { L } \right]$ .
C) Carla,because $[ \vec { v } ] = \left[ \frac { L } { T } \right]$ .
D) Carla,because $[ \overrightarrow { \mathrm { v } } ] = \left[ \frac { \mathrm { L } } { \mathrm { MT } } \right]$ .
E) Spike,because the dimensions of force are $[ \overrightarrow { \mathrm { F } } ] = \left[ \frac { \mathrm { T } ^ { 2 } } { \mathrm { ML } } \right]$ .