Question

How do you convert km/h to m/s?

Answer 1

Use dimensional analysis (a.k.a. factor-label method).

Explanation:

Given:

`(x" km")/"h"`

Multiply by the conversion factor `(1000" m")/(1" km")`:

`(xcancel(" km"))/"h"xx(1000" m")/(1cancel(" km"))`

Please observe how the km units cancel.

Multiply by the conversion factor `(1" h")/(3600" s")`

`(xcancel(" km"))/cancel("h")xx(1000" m")/(1cancel(" km"))xx(1cancel(" h"))/(3600" s")`

Please observe that the hour units are canceled and we are left with the units of `"m/s"`.

Follow the rules of the multiplication of fractions to obtain the value of `x`:

`(xcancel(" km"))/cancel("h")xx(1000" m")/(1cancel(" km"))xx(1cancel(" h"))/(3600" s") = (5x)/18\ "m/s"`

Answer 2

Let's convert 10km/h to m/s.

`"10 km = 10,000 m"`

`"1 hour = 60 min"`

`"1 min = 60 s"`

`("10km")/("1h") = ("10,000 m")/("60"*"60s")`

`=(10,000)/3600`

`="2.78 ms"^(-1)`

Answer 3

Divide by `3.6`

Explanation:

There are `1000` meters in a kilometer, so:

`1` km/h is `1000` m/h#

In one minute you would travel `1/60`th of that, so:

`1000/60` m/minute.

In one second you would travel `1/60`th of that, so:

`1000/(60xx60) = 1000/3600 = 1/3.6` m/s

In summary:

`1` km/h `= 1/3.6` m/s

So to convert from km/h to m/s, divide by `3.6`

Note that dividing by `3.6` is the same as dividing by `4` then adding `11.bar(1)` %. So for a quick approximation, halve the original number twice, then add `10` %. If you want more accuracy, add `10` % and `1` %, etc.

For example:

`10` km/h `-> 5 -> 2.5 -> 2.5+0.25+0.025+... = 2.777...` m/s