How to Convert km/h to m/s – Formula, Trick

The concept of speed or velocity is one of the most important concepts in both Physics and Mathematics world. We often hear terms like the speed of the bike is 60 km/h or the velocity of the train is 200 km/h. These are expressions of the magnitude of the speed in different units. The velocity is measured generally in m/s or km/h. It is important to note that the standard unit of representation of speed or velocity in physics is m/s. Here, m/s refers to a meter per second while km/h refers to kilometer per hour. In this article, we will understand how to convert km/h to m/s using its formula and trick.

How to Convert km/h to m/s

It is often seen that despite knowing the concept of a particular topic, students make mistakes in solving its problems due to difference in units. It is important to understand that we can compare, add, or subtract only those quantities whose units are same. For example, if we are to compare the speed of a bus and train given as 10 m/s and 70 km/h, then we will have to bring them to a common unit. So we will have to either convert m/s in km/h or km/h to m/s. Before learning how to convert km/h to m/s, let us understand what are these units and where do they come from.

Concept of km/h and m/s

Km/h and m/s are the units of speed/velocity. Velocity or speed is the ratio of total distance covered and total time taken. That is, speed = distance/time. The value of distance can be either expressed in km (kilometer) or meter(m) while time can be expressed in hour (h), minute (m), or second (s). So, when the distance is in kilometer and time is in hour, then the unit of speed becomes km/h (kilometer/hour). When the distance is given in meter and time is given in second, the unit of speed becomes m/s (meter/second).

Hence, km/h means the number of kilometers travelled by an object in 1 hour and m/s means the distance covered in meters in 1 second.

How to Convert km/h to m/s Formula

It is often required to convert one unit into another for the ease of calculation. The conversion of units is an important concept in physics and mathematics. We can convert one unit into another  by knowing the basic relation between their equivalence. We use the multiplication to convert a higher order unit into a lower order unit and divide in the opposite case.

For example, 1 km = 1000 m

1 h = 60 x 60 s  = 3600 s

The same has been illustrated in the following diagram.

As, we can see from the above relation, when we convert higher order unit (km or h) to lower unit (m or s) we multiply by the equivalent magnitude and divide in the opposite case. So, to change km/h to m/s, we multiply the given unit by a conversion factor of 1000/3600. Hence the conversion formula for km/h to m/s becomes:

1 km/h = (1000/3600) m/s

Hence, we can get m/s from km/h by multiplying the value with 1000/3600.

How to Convert km/h to m/s Trick

We can use the trick to convert a given value in km/h to m/s using the trick. The trick is to multiply the given value by 5/18. That is,

1 km/h = (5/18) m/s

Using this trick, one can easily derive the value of m/s from km/h.

How to Convert km/h to m/s Steps

One can convert the value of km/h to m/s by using the steps given below.

Step 1: If the value of distance is given in km, then multiply it by a factor of 1000 or 5

Step 2: Multiply the time value by 3600 or 18, in case the time value is given in hour

Step 3: Reduce the obtained fractional result

How to Convert km/h to m/s Examples

Some solved problems on this topic is given below. These solved examples will help students understand this topic in a better way.

Example 1: Given the speed of a car is 72 km/h and the speed of the bus is 16 m/s. Which one is faster?

Solution: As we know that only those quantities can be compared, that have similar values.

Hence, using the conversion formula for m/s, we will convert the speed of bus in m/s.

so, 72 km/h = 72 x 1000/3600

=> 72 x 10/36

= 20 m/s

Hence, the speed of car = 20 m/s

as the speed of car > speed of bus

so, car is faster than the bus.

Example 2: What will be the value 2 km/s in m/s?

Solution: We have been given 2 km/s

as we know, 1 km = 1000 m

so, 2 km = 2000 m

so, 2 km/s = 2000 m/s

Example 3: Determine the given value of 18000 m /h in m/s

Solution: We have been given, 18000 m/h

as 1 h = 3600 s

so, 18000 m/h = 18000 m/ 3600 s

or, 18000 m/h = 5 m/s

Example 4: The distance covered by a moving truck in 1 hour is 108 kilometer. Determine the speed of the given truck in SI unit.

Solution: We have been given distance = 108 km

time = 1 h

SI unit of speed is expressed in meter/second

as, speed = distance/time

so, speed = 108/1

speed = 108 km/h

for converting it into m/s, we will use the trick of multiplying the given value by 5/18

so, 108 km/h = 108 x 5/18 m/s

=> 6 x 5 m/s

= 30 m/s

Hence, speed in SI unit = 30 m/s

Example 5: Find out the distance of the object in meter if the speed is given to be 5 km/h and the time is 2 hour. 

Solution: As we know, speed = distance/time

given speed = 5 km/h

time = 2 hour

substituting these values in the equation of speed, we get

5 = distance/2

or, distance = 5 x 2

as the speed is in km/h and time is in h, so we get the distance in km

hence, distance = 10 km

as we know, 1 km = 1000 m

so by using this conversion factor, we get

Distance = 10 x 1000

Distance = 10,000 meter

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