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

Question

Quizplus · Accepted Answer

Using dimensional analysis, we can determine the dimensions of velocity, which are length/time. We can then use the given variables, mass (m), time (t), and force (F), to see which expression for change in velocity is correct.

Starting with Spike's expression: 
11eb8b15_7528_e39c_8952_dbf04e4132a1_TB8845_11

If we break down the dimensions of each variable: 
- m: [M]
- t: [T]
- F: [M][L]/[T]^2

We can substitute these into the expression: 
11eb8b15_7528_e39c_8952_dbf04e4132a1_TB8845_11  = [M][L]/[T]^2 / [M][T] 
Simplifying, we get: [L]/[T], which is the correct dimension of velocity.

However, Carla argues that the dimensions of force are incorrect in Spike's expression. If we break down the dimensions of force: 
- F: [M][L]/[T]^2

We can see that Carla is correct, and the dimensions of force in Spike's expression are incorrect.

Checking Carla's expression: 
11eb8b15_7529_31c1_8952_17d2775d31be_TB8845_11

If we break down the dimensions of each variable: 
- m: [M]
- t: [T]
- F: [M][L]/[T]^2

We can substitute these into the expression: 
11eb8b15_7529_31c1_8952_17d2775d31be_TB8845_11  = [M][L]/[T]^2 / [M] 
Simplifying, we get: [L]/[T]^2, which is incorrect for velocity.

Therefore, the correct answer is C) Carla, because the dimensions of force are 11eb8b15_7529_31c1_8952_17d2775d31be_TB8845_11.

Spike Claims That Dimensional Analysis Shows That the Correct Expression v⃗f−v⃗i\vec{v}_{f}-\vec{v}_{i}vf​−vi​

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