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 is $\vec{v}_{f}-\vec{v}_{i}$ , is $\overrightarrow{\mathrm{v}}_{f}-\overrightarrow{\mathrm{v}}_{i}=\frac{m t}{F}$ , 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 $[\overrightarrow{\mathrm{v}}]=\left[\frac{\mathrm{ML}}{\mathrm{~T}}\right]$ .
B) Spike, because $[\overrightarrow{\mathrm{v}}]=\left[\frac{\mathrm{T}^{2}}{\mathrm{~L}}\right]$ .
C) Carla, because $[\overrightarrow{\mathrm{v}}]=\left[\frac{\mathrm{L}}{\mathrm{~T}}\right]$ .
D) Carla, because $[\overrightarrow{\mathrm{V}}]=\left[\frac{\mathrm{L}}{\mathrm{MT}}\right]$ .
E) Spike, because the dimensions of force are $[\overrightarrow{\mathrm{F}}]=\left[\frac{\mathrm{T}^{2}}{\mathrm{ML}}\right]$ .