Example 4
Convert an acceleration of $10 \mathrm{~ms}^{-2}$ to a value in $\mathrm{kmh}^{-2}$

Step 1 ：The acceleration is given in meters per second squared (ms^-2). We need to convert it to kilometers per hour squared (kmh^-2).

Step 2 ：To do this, we need to convert meters to kilometers and seconds to hours.

Step 3 ：1 meter = 0.001 kilometers

Step 4 ：1 second = 1/3600 hours

Step 5 ：So, we need to multiply the given acceleration by (0.001/1) for the distance conversion and by (1/3600)^2 for the time conversion.

Step 6 ：\(acceleration_{ms^2} = 10\)

Step 7 ：\(m_{to_{km}} = 0.001\)

Step 8 ：\(s_{to_{h}} = 0.0002777777777777778\)

Step 9 ：\(acceleration_{kmh^2} = 129600.0\)

Step 10 ：Final Answer: The acceleration in kmh^-2 is \(\boxed{129600}\).