How do I properly convert from km/h to m/s?

[menco]

Homework Statement

I am confusing myself when converting from km/h to m/s

I understand that if you have 100km/h you take 100 * 1000 / 3600 = 27.78m/s

But where i get confused is if you have 1km and you want meters you *1000 but if you have 1hr and you want seconds you also have to *3600 (not divide)

I'm sure I'm just looking at it the wrong way can someone explain it better?

 

[ehild]

Think: you travel 100 km in a hour: it is 100*1000 =100000 m in a hour.
How far do you get in 1 s? Is it longer or shorter time then one hour? Is the distance traveled longer or shorter? There is 3600 s in a hour. The second is 1/3600-th of an hour. So the distance traveled in 1 s is ?...

ehild

 

[phyzguy]

One technique that I've found helps students get these problems right is to "multiply by one". In any expression, you can multiply it by one as many times as you want without changing it. So you set up ratios which are equal to one and multiply by as many of them as you need to get the units you want, as follows:

$$100 \frac{km}{hr} * \frac{1000 m}{1km} * \frac{1 hr}{3600 sec} = 27.7 \frac{m}{sec}$$

Then you cancel out the units to get what you want. You can do this as many times as you need. For example if you want cm/sec, you can do this:

$$100\frac{km}{hr}*\frac{1000 m}{1km}*\frac{100 cm}{1 m}*\frac{1 hr}{3600 sec} = 2770 \frac{cm}{sec}$$

Hope this helps.

 

[Hobin]

But where i get confused is if you have 1km and you want meters you *1000 but if you have 1hr and you want seconds you also have to *3600 (not divide)

That's because you multiply a value in the denominator. In other words, value/h = value/((h*3600)s)