To know **how to convert from km/ham/s** it is necessary to do a mathematical operation in which the equivalences between kilometers and meters, and between hours and seconds are used.

The method that will be used to convert from kilometers per hour (km/h) to meters per second (m/s) can be applied to transform a certain unit of measurement into another, as long as the respective equivalences are known.

When going from km/ham/s, two conversions of units of measurement are being made. This is not always the case, as you may have a case where only one unit of measure needs to be converted.

For example, if you want to go from hours to minutes, you are only converting, just like when you convert from meters to centimeters.

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**Basics of converting from km/ham/s**

The first thing you need to know is the equivalence between these units of measurement. That is, one must know how many meters there are in a kilometer and how many seconds there are in an hour.

These conversions are as follows:

– 1 kilometer represents the same length as 1000 meters.

– 1 hour is 60 minutes, and each minute consists of 60 seconds. Therefore, 1 hour is 60*60=3600 seconds.

**Conversion**

It starts from the assumption that the quantity to be converted is X km/h, where X is any number.

To go from km/ham/s you must multiply the entire quantity by 1000 meters and divide by 1 kilometer (1000 m/1 km). Also, it must be multiplied by 1 hour and divided by 3600 seconds (1 h/3600 s).

It is in the previous process where the importance of knowing the equivalences between the measures lies.

Therefore, X km/h is the same as:

X km/h *(1000 m/1 km)*(1 h/3,600 s) = X*5/18 m/s = X*0.2777 m/s.

The key to performing this measurement conversion is:

– Divide by the unit of measure that is in the numerator (1 km) and multiply by the equivalent unit to which you want to transform (1000 m).

– Multiply by the unit of measure that is in the denominator (1 h) and divide by the equivalent unit to which you want to transform (3600 s).

**solved exercises**

**First exercise**

A cyclist is going 18 km/h. How many meters per second is the cyclist going?

To answer it is necessary to convert the units of measurement. Using the above formula it turns out that:

18 km/h = 18*(5/18) m/s = 5 m/s.

Therefore, the cyclist is going at 5 m/s.

**second exercise**

A ball is rolling downhill at a speed of 9 km/h. How many meters per second is the ball rolling?

Again, using the above formula, you have:

9 km/h = 9*(5/18) m/s = 5/2 m/s = 2.5 m/s.

In conclusion, the ball is rolling at 2.5 m/s.

### third exercise

On an avenue there are two vehicles, one red and one green. The red car is traveling at 144 km/h and the green car is traveling at 42 m/s. Which vehicle travels faster?

In order to answer the question asked, both speeds must be in the same unit of measure, in order to be able to compare them. Either of the two conversions is valid.

Using the formula written above, the speed of the red vehicle can be taken as am/s as follows:

144 km/h = 144*5/18 m/s = 40 m/s.

Knowing that the red car is traveling at 40 m/s, it can be concluded that the green car is traveling faster.

The technique used to convert from km/ham/s can be applied in a general way to convert units of measurement into others, always keeping in mind the respective equivalences between the units.

**fourth exercise**

A train travels at 162 km/h, how many meters will it travel in 1 hour?

In this case, to solve the exercise we must apply the previous formula to find the m/s at which the train goes.

162 km/h = 162*(5/18) m/s = 45 m/s.

Since the train travels 45 m/s and we want to find out how many meters it travels in one hour, we must multiply 45 by 60 minutes by 60 seconds:

45*60*60=162,000m/h

That is, in one hour the train will travel 162,000 meters.

**References**

Barrantes, H., Diaz, P., Murillo, M., & Soto, A. (1988). *Introduction to Number Theory.* San Jose: EUNED.

Bustillo, A.F. (1866). *Mathematics Elements.* from Santiago Aguado.

Guevara, MH (nd). *Number Theory.* San Jose: EUNED.

AC, & A., LT (1995). *How to Develop Mathematical Logical Reasoning.* Santiago de Chile: University Editorial.

Jiménez, J., Delgado, M., & Gutiérrez, L. (2007). *Guide Think II.* Threshold Editions.

Jiménez, J., Teshiba, M., Teshiba, M., Romo, J., Álvarez, M., Villafania, P., Nesta, B. (2006). *Mathematics 1 Arithmetic and Pre-Algebra.* Threshold Editions.

Johnsonbaugh, R. (2005). *Discrete mathematics.* Pearson Education.