Which expression is dimensionally consistent with an expression that would yield a
value for time ? ( is velocity, is distance, and is time)

Ask by Dickson Kelley. in the United States

Jan 27,2025

Question

Which expression is dimensionally consistent with an expression that would yield a
value for time ? ( is velocity, is distance, and is time)

Ask by Dickson Kelley. in the United States

Jan 27,2025

UpStudy AI · Accepted Answer

To determine which expression is dimensionally consistent with yielding a value for time $$ { }^{-1} $$ (i.e., units of $$ \text{T}^{-1} $$), we'll analyze the dimensions of each given option.

**Given:**
- **Velocity ($$ v $$)** has dimensions: $$[L][T]^{-1}$$
- **Distance ($$ x $$)** has dimensions: $$[L]$$
- **Time ($$ t $$)** has dimensions: $$[T]$$

**Analyzing Each Option:**

1. **$$ \frac{v}{x} $$**
   $$
   \frac{[L][T]^{-1}}{[L]} = [T]^{-1}
   $$
   **Dimensions:** $$ \text{T}^{-1} $$

2. **$$ \frac{v^{2}}{x} $$**
   $$
   \frac{([L][T]^{-1})^{2}}{[L]} = \frac{[L]^2 [T]^{-2}}{[L]} = [L][T]^{-2}
   $$
   **Dimensions:** $$ \text{L}\text{T}^{-2} $$

3. **$$ \frac{x}{t} $$**
   $$
   \frac{[L]}{[T]} = [L][T]^{-1}
   $$
   **Dimensions:** $$ \text{L}\text{T}^{-1} $$

4. **$$ v^{2} t $$**
   $$
   ([L][T]^{-1})^{2} [T] = [L]^2 [T]^{-2} [T] = [L]^2 [T]^{-1}
   $$
   **Dimensions:** $$ \text{L}^2\text{T}^{-1} $$

5. **$$ \frac{x}{v} $$**
   $$
   \frac{[L]}{[L][T]^{-1}} = [T]
   $$
   **Dimensions:** $$ \text{T} $$

**Conclusion:**

Only **option 1** ($$ \frac{v}{x} $$) has the dimensions $$ \text{T}^{-1} $$, making it the correct choice.

**Answer:**  
1) $$ v / x $$
$$ \frac{v}{x} $$ is dimensionally consistent with time $$ { }^{-1} $$.

Which expression is dimensionally consistent with an expression that would yield a
value for time ? ( is velocity, is distance, and is time)

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Which expression is dimensionally consistent with an expression that would yield a value for time ? ( is velocity, is distance, and is time)

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Which expression is dimensionally consistent with an expression that would yield a
value for time ? ( is velocity, is distance, and is time)