Convert an acceleration of 100 m/s² into km/hr².

Steps to Solve

1. Identify the conversion factors

To convert from meters to kilometers, use the fact that 1 kilometer equals 1000 meters. To convert from seconds squared to hours squared, note that there are 3600 seconds in one hour, so we will need to square this conversion factor.

2. Convert the meters to kilometers

For the acceleration in m/s², to convert it to km/hr², we use the conversion:

$$ 1 , \text{m/s}^2 = \frac{1 , \text{km}}{1000 , \text{m}} $$

We will multiply by 1000 to account for the conversion from m to km.

3. Convert the seconds to hours

Now, we need to convert the time component from seconds to hours squared. This can be done using:

$$ 1 , \text{s}^2 = \left( \frac{1 , \text{hr}}{3600 , \text{s}} \right)^2 = \frac{1 , \text{hr}^2}{3600^2 , \text{s}^2} $$

So, we multiply by $3600^2$ when converting from seconds squared to hours squared.

4. Combine the conversions

Putting it all together for the conversion of acceleration from m/s² to km/hr²:

$$ 1 , \text{m/s}^2 = \frac{1 , \text{km}}{1000 , \text{m}} \times 3600^2 , \text{hr}^2 $$

5. Calculate the final conversion factor

Calculate $3600^2$:

$$ 3600^2 = 12960000 $$

Now we can write the final conversion factor:

$$ 1 , \text{m/s}^2 = \frac{12960 , \text{km}}{1 , \text{hr}^2} $$

Thus,

$$ 1 , \text{m/s}^2 = 12960 , \text{km/hr}^2 $$