When calculating speed, you may occasionally need to convert between units of length or between units of time. This becomes a little trickier when you need to convert between different speeds.
Kilometres per hour to metres per second
You need to remember to change both of the units here. Kilometres are converted to metres by multiplying by $1000$1000. Hours are converted to seconds by multiplying by $3600$3600.
If you wanted to convert 4 kilometres per hour to metres per second you would need to do:
$\frac{4\times1000}{1\times3600}$4×10001×3600 = $\frac{4000}{3600}$40003600 = $1.1111$1.1111 m/s
Sometimes when I work out these conversions I think about it vertically, and I concentrate on the units. I can do it piece by piece.
Here is the same question done in a different way.
| $4$4 km/h | $=$= | $4000$4000metres/$60$60 minutes | writing the $4$4 km as meters, and the $1$1 hour as minutes |
| $=$= | $400$400 meters / $6$6 minutes | simplifying a little | |
| $=$= | $200$200 meters / $3$3 minutes | simplifying a bit more | |
| $=$= | $200$200 meters / 180 seconds | because $3$3 minutes is the same as $3\times60$3×60 seconds | |
| $=$= | $20$20 meters / $18$18 seconds | simplify | |
| $=$= | $10$10 meters / $9$9 seconds | simplify | |
| $=$= | $1.11$1.11m/s | calculate |
Worked Examples
Question 1
Convert the following amounts into the units required, writing your answers correct to 2 decimal places where necessary:
$2500$2500 metres into kilometres
$2100$2100 seconds into minutes
$45$45 km/h into m/s
$7.562$7.562 kilometres into metres
$6.85$6.85 hours into seconds
$14$14 m/s into km/h
Question 2
If a sugar glider possum travels $6$6 km at a speed of $15$15 km/hr, how long will it take the animal to cross the whole distance?
Question 3
A dog travels $42$42 km in $1.4$1.4 hours.
At what speed is it travelling?