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

question 18

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 \([\overrightarrow{\mathrm{F}}]=\left[\frac{\mathrm{T}^{2}}{\mathrm{ML}}\right]\) .

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