One foot per second is exactly 0.3048 metres per second. The factor is the same as for the lengths themselves, because both are divided by the same second — and unlike most imperial conversions, this one is exact with no repeating decimal.
About the units
The foot per second is the American engineering unit for velocities where the mile per hour would be too coarse, and it dominates two fields in particular: ballistics and fluid flow. The metre per second is the SI unit. Because the foot has been exactly 0.3048 metres since 1959, the conversion terminates cleanly in one direction — feet per second to metres per second — and repeats in the other, at 3.280839895 ft/s per m/s.
The exact factor
The factor is exactly 0.3048. Reference values from ballistics make the scale concrete: a subsonic pistol round leaves the barrel at about 1,000 ft/s, or 305 m/s; a common rifle cartridge at 3,000 ft/s, or 914 m/s; and the speed of sound at sea level is 1,116 ft/s or 340 m/s, which is the threshold that determines whether a projectile produces a sonic crack. In fluid work, pipe velocities are typically kept below 10 ft/s or 3 m/s to limit erosion and noise.
Where you meet this conversion
Ballistics above all, where muzzle velocity is quoted in feet per second in American sources and metres per second in European, and the same cartridge therefore appears with two very different numbers. Plumbing and process piping specify flow velocity in feet per second in American codes. Aerodynamics, conveyor speeds and free-fall calculations in American engineering all use it. Anyone comparing an American cartridge specification to a European one needs this factor before drawing any conclusion about performance.