The ×3.6 bridge
Physics thinks in ; the road signs outside think in . The bridge between them is exact and friendly: an hour is 3600 seconds, a kilometre is 1000 metres, and . So — m/s to km/h multiplies by 3.6, km/h to m/s divides.
Never sure which way? The numbers themselves will tell you: for the same real speed, the km/h number is always the BIGGER one — a 10 m/s sprinter is doing 36 km/h. If your conversion made the km/h number smaller, you crossed the bridge backwards. Turn around and cross again.
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