Convert 40 mph to meters per second.

Steps to Solve

1. Identify the conversion factor for speed

To convert from miles per hour (mph) to meters per second (m/s), we need to know the conversion factors for miles to meters and for hours to seconds.

1 mile is approximately equal to 1609.34 meters, and 1 hour is equal to 3600 seconds.

So, the conversion factor from mph to m/s is:

$$ \frac{1609.34 \text{ meters}}{3600 \text{ seconds}} $$

2. Set up the conversion formula

To convert a speed given in mph (let's say ( v ) mph) to m/s, we can set up the following formula:

$$ v \text{ (m/s)} = v \text{ (mph)} \times \frac{1609.34 \text{ meters}}{3600 \text{ seconds}} $$

3. Perform the conversion multiplication

Now, if you have a specific speed (for example, ( v = 60 ) mph), plug that value into the formula:

$$ v \text{ (m/s)} = 60 \text{ mph} \times \frac{1609.34 \text{ meters}}{3600 \text{ seconds}} $$

Calculating this we have:

$$ v \text{ (m/s)} = 60 \times \frac{1609.34}{3600} $$

4. Calculate and simplify

Now perform the calculations:

$$ \frac{1609.34}{3600} \approx 0.44704 $$

Therefore,

$$ v \text{ (m/s)} \approx 60 \times 0.44704 \approx 26.8224 $$

So,

$$ 60 \text{ mph} \approx 26.82 \text{ m/s} $$