One metre per second is 2.2369362921 miles per hour. The number is 3.6 divided by 1.609344 — the metric conversion followed by the mile conversion — and it is the bridge between SI physics and American everyday speeds.
About the units
The metre per second is the SI unit of speed and what every mechanics equation requires. The mile per hour is the road unit in the United States and the United Kingdom. Converting between them means crossing both a time unit and a distance unit at once, which is why the factor is untidy where the metric equivalent is a clean 3.6. Note that a mile per hour is exactly 0.44704 metres per second, an exactly defined value since both the mile and the hour are exactly defined.
The exact factor
The exact reciprocal is 1 mph = 0.44704 m/s. Useful anchors: 10 m/s is 22.4 mph, 20 m/s is 44.7 mph, and 45 m/s is 100.7 mph. For a rough mental method, doubling and adding a fifth works — 15 m/s gives 30 plus 3, which is 33 against the true 33.6. Terminal velocity for a skydiver in a belly-down position is about 55 m/s, or 123 mph, which is the figure behind most published free-fall speeds.
Where you meet this conversion
Physics and engineering in American contexts, where a calculation must run in SI but the inputs and outputs are quoted in miles per hour. Impact and crash analysis, projectile motion and wind loading all work this way. Meteorology in the United States reports wind in miles per hour while the models behind the forecast compute in metres per second. Sports science measures sprint and pitch speeds in metres per second and reports them in miles per hour for American audiences.