One metre per second is exactly 3.6 kilometres per hour. The 3.6 is the single most useful number in the speed category: it is 3,600 seconds per hour divided by 1,000 metres per kilometre, and it converts between the physicist's unit and the driver's.
About the units
The metre per second is the SI unit of speed, and every equation in mechanics expects it — kinetic energy, momentum, drag and acceleration all break if a speed arrives in kilometres per hour. The kilometre per hour is what road signs, speedometers and weather reports use, because human-scale speeds come out as convenient two- and three-digit numbers. Neither is more correct; they belong to different tasks. The conversion between them is the boundary every physics problem about a car has to cross.
The exact factor
The factor is exactly 3.6, and it is worth memorising in both directions: multiply by 3.6 going from m/s to km/h, divide by 3.6 coming back. Useful anchors: 10 m/s is 36 km/h, 25 m/s is 90 km/h, and 30 m/s is 108 km/h. Wind speed thresholds become legible this way — gale force 8 begins at 17.2 m/s, which is 62 km/h, and hurricane force 12 at 32.7 m/s, which is 118 km/h. A pedestrian walks at about 1.4 m/s, or 5 km/h.
Where you meet this conversion
Physics and engineering calculations that start from a real-world speed. Braking distance, impact energy and aerodynamic drag all require metres per second, and every one of those calculations begins by dividing a posted speed by 3.6. Meteorology reports wind in metres per second in the Nordic countries and much of Europe while giving it in kilometres per hour elsewhere, so the same forecast reads differently across a border. Athletics converts race times into metres per second to compare performances across distances.