3 Converting units

1 km/h = 1000 m / 3600 s = 5/18 m/s. So multiply km/h by 5/18 to get m/s; multiply m/s by 18/5 (= 3.6) to get km/h.

Examples:

• 36 km/h = 36 × 5/18 = 10 m/s.
• 25 m/s = 25 × 3.6 = 90 km/h.

Example 1. A cyclist covers 450 m in 90 s along a straight road. Find the velocity in m/s and in km/h. v = Δd/Δt = 450/90 = 5 m/s; in km/h: 5 × 3.6 = 18 km/h.

Example 2. A train moves at a velocity of 72 km/h. How far does it go in 25 min if the velocity is uniform? 72 km/h = 20 m/s; t = 25 × 60 = 1500 s; Δd = vΔt = 20 × 1500 = 30 000 m = 30 km. (Or in km/h: 72 × 25/60 = 30 km.)

Example 3. An athlete runs 6000 m in 40 min along a straight track. The average velocity is 6000/(40 × 60) = 2.5 m/s = 9 km/h. If he keeps this average velocity he covers 2.5 × 3600 = 9000 m in one hour.