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)

 

[asteriatic]

I completely understand your confusion with converting from km/h to m/s. It can be a bit tricky at first, but with practice, it will become second nature. To help clarify, let's break down the conversion process step by step.

First, it's important to remember that km/h and m/s are both units of speed. Km/h stands for kilometers per hour, while m/s stands for meters per second. The key difference between the two is the unit of distance (km vs m) and the unit of time (hour vs second).

When converting from km/h to m/s, we need to take into account the different units of distance and time. As you correctly stated, if we have 100km/h, we can convert it to m/s by multiplying 100 by 1000 (to convert from km to m) and then dividing by 3600 (to convert from hours to seconds). This gives us a final answer of 27.78m/s.

Now let's look at your example of 1km. If we want to convert this to meters, we simply multiply by 1000, as you mentioned. However, if we want to convert 1 hour to seconds, we need to multiply by 3600, not divide. This is because we are converting from a larger unit (hours) to a smaller unit (seconds), so we need to multiply.

In summary, when converting from km/h to m/s, we need to keep in mind the different units of distance and time and use the appropriate conversion factors (multiplying or dividing) to get the correct answer. With practice, you will become more comfortable with these conversions. I hope this explanation helps clear up any confusion you may have had.