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The problem asks to convert \(\frac{m}{s^2}\) to \(\frac{k}{hr^2}\) using dimensional analysis. Here's the complete solution:

### Step 1: Identify the units to convert

You are converting from meters per second squared (\(\frac{m}{s^2}\)) to kilometers per hour squared (\(\frac{k}{hr^2}\)).

1. **Meters (m) to Kilometers (k)**:  
   \(1 \text{ kilometer} = 1000 \text{ meters}\)
   
2. **Seconds (s) to Hours (hr)**:  
   \(1 \text{ hour} = 3600 \text{ seconds}\)

### Step 2: Set up the conversion for each unit

To convert \(\frac{m}{s^2}\) to \(\frac{k}{hr^2}\), you need to perform the following conversions:

#### 1. Convert meters to kilometers:
\[
\frac{1 \text{ kilometer}}{1000 \text{ meters}} = \frac{1}{1000}
\]

#### 2. Convert seconds squared to hours squared:
Since \(1 \text{ hour} = 3600 \text{ seconds}\), we have:
\[
\left(\frac{3600 \text{ seconds}}{1 \text{ hour}}\right)^2 = \frac{(3600)^2 \text{ seconds}^2}{1 \text{ hour}^2} = \frac{12960000 \text{ seconds}^2}{1 \text{ hour}^2}
\]

### Step 3: Multiply the conversion factors

Now, multiply the original unit \(\frac{m}{s^2}\) by the conversion factors for both meters to kilometers and seconds squared to hours squared:

\[
\frac{m}{s^2}

Convert m/s^2 to k/hr^2 using DIMENSIONAL ANALYSIS. Show your complete solution.

Learn how to convert meters per second squared (m/s^2) to kilometers per hour squared (k/hr^2) using dimensional analysis. This step-by-step guide includes the conversion of meters to kilometers and seconds to hours squared, using key unit conversion principles. Suitable for high school students studying physics or dimensional analysis.

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