Instruments for measuring vehicle speed measure speed in kilometers per hour. In the system, it is customary to measure speed in meters per second. We will analyze how to translate speeds into the system system.

**Notes: **

## Kilometers per hour in meters per second

Consider two ways to transfer units, one - using the formula, the second - using a predetermined list.

### Method 1 - using the formula

\ [\ Large \ Boxed {v_ {m} = v_ {k} \ Cdot \ FRAC {1000} {3600}} \]

\ (\ displaystyle v_ {k} \ left (\ frac {\ text {km}} {\ text {h}} \ right) \) - speed expressed in kilometers per hour;

\ (\ displaystyle v_ {m} \ left (\ frac {\ text {m}} {c} \ right) \) - speed, expressed in meters per second;

One kilometer is placed 1000 meters.

One hour contains 3600 seconds.

**Example 1. **. The plane moves at a speed of 420 kilometers per hour. Transfer this speed to meters per second.

**Decision: **

\ [\ large v_ {m} = 420 \ CDOT \ FRAC {1000} {3600} \]

For convenience, lay the numbers on multipliers:

\ [\ LARGE V_ {M} = 6 \ CDot 7 \ CDOT 10 \ CDOT \ FRAC {10} {6 \ CDOT 6} \]

We will reduce and get an accurate answer:

\ [\ LARGE V_ {M} = 7 \ CDOT 10 \ CDOT \ FRAC {5} {3} = \ FRAC {350} {3} \]

In some cases, the accurate answer can be rounded:

**Answer: **

\ [\ displaystyle \ large v_ {m} = 116 {,} 67 \ left (\ FRAC {\ Text {m}} {C} \ Right) \]

### Method 2 - using the list

Kilometers per hour in meters per second can be quickly translated into the mind, applying such a list:

\ [\ Large \ Boxed {\ Begin {Matrix} 3 {,} 6 \ Left (\ FRAC {\ Text {km}} {h} \ right) = 1 \ left (\ frac {\ text {m}} { C} \ Right) \\ 7 {,} 2 \ left (\ FRAC {\ Text {km}} {h} \ right) = 2 \ left (\ FRAC {\ Text {m}} {C} \ Right) \\ 10 {,} 8 \ left (\ frac {\ text {km}} {h} \ right) = 3 \ left (\ FRAC {\ Text {m}} {C} \ Right) \\ 14 {, } 4 \ left (\ frac {\ text {km}} {h} \ right) = 4 \ left (\ FRAC {\ Text {m}} {C} \ Right) \ end {Matrix}} \]

\ [\ Large \ Boxed {\ Begin {Matrix} 18 \ Left (\ FRAC {\ Text {km}} {h} \ Right) = 5 \ left (\ FRAC {\ Text {M}} {C} \ Right ) \\ 36 \ left (\ frac {\ text {km}} {h} \ Right) = 10 \ left (\ FRAC {\ Text {m}} {C} \ Right) \\ 54 \ Left (\ FRAC {\ text {km}} {h} \ Right) = 15 \ left (\ FRAC {\ Text {m}} {C} \ Right) \\ 72 \ left (\ FRAC {\ text {km}} {h } \ Right) = 20 \ left (\ FRAC {\ Text {M}} {C} \ Right) \ end {Matrix}} \]

**Example 2. **. The car is moving along the highway at a speed of 108 kilometers per hour. Transfer this speed to meters per second.

**Decision: **

108 km / h = 72 km / h + 36 km / h = 20 m / s + 10 m / s

**Answer: **

108 km / h = 30 m / s

## Transfer meters per second back to kilometers per hour

Sometimes there is a need to translate the speed of meters per second to kilometers per hour. To do this, we use such a formula:

\ [\ Large \ Boxed {v_ {m} \ Cdot \ FRAC {3600} {1000} = V_ {k}} \]

## Speed of slower objects

The speed of movement of slow objects, for example, some living beings - snails, is measured at centimeters per minute. Translate such units into the system also, easy enough.

\ [\ Large \ Boxed {v_ {m} = v_ {s} \ Cdot \ FRAC {0.01} {60}} \]

\ (\ displaystyle v_ {s} \ left (\ frac {\ text {km}} {\ text {h}} \ right) \) - speed expressed in centimeters per minute;

\ (\ displaystyle v_ {m} \ left (\ frac {\ text {m}} {c} \ right) \) - speed, expressed in meters per second;

100 centimeters are placed in one meter. And 1 centimeter is 0.01 meters.

One minute contains 60 seconds.

**Example 3. **. Snail moves at a speed of 6 centimeters per minute. Transfer this speed to meters per second.

**Decision: **

\ [\ Large v_ {m} = 6 \ Cdot \ FRAC {0.01} {60} \]

Unlock numbers for factors:

\ [\ LARGE V_ {M} = 6 \ Cdot \ FRAC {0.01} {6 \ CDOT 10} \]

Sperate numbers and get the answer:

**Answer: **

\ [\ displaystyle \ large v_ {m} = 0 {,} 001 \ left (\ FRAC {\ Text {m}} {C} \ Right) \]

Fig. 1. The snail moves quite slowly by human standards, its speed is approximately equal to one millimeter per second

## findings

To transfer the speed to the SI system, you can use any convenient reception - or use the translation formula, or, prepare a list of some speeds in advance, and then present the transmitted speed as a sum, folding numbers from the list;

How to translate meters per second to kilometers per hour (m / s in km / h)?

To replace meters per second to kilometers per hour, you need to translate meters to kilometers, and seconds - in hours:

Thus, 1 m / s is 3.6 km / h or 18/5 km / h.

It means to translate meters per second to kilometers per hour, it is necessary to multiply a number of meters per second by 3.6 kilometers per hour (or by 18/5 km / h).

M / s translation formula in km / h:

It is not necessary to memorize this formula - in stressful conditions of the exam or control operation, memory may result. Reliable to withdraw it every time, expressing meters in kilometers, and seconds in the clock.

Translation of meters per second to kilometers per hour Consider on specific examples.

Examples .

*Express meters per second in kilometers per hour: *

*1) 5 m / s; *

*2) 10 m / s; *

*3) 12 m / s; *

*4) 18 m / s; *

*5) 23.5 m / s; *

*6) 30.4 m / s. *

Decision :

1) 5 m / s = 5 ∙ 3600/1000 km / h = 5 ∙ 18/5 km / h = 18 km / h;

2) 10 m / s = 10 ∙ 3600/1000 km / h = 10 ∙ 3.6 km / h = 36 km / h;

3) 12 m / s = 12 ∙ 3600/1000 km / h = 12 ∙ 3.6 km / h = 43.2 km / h;

4) 18 m / s = 18 ∙ 3600/1000 km / h = 18 ∙ 3.6 km / h = 64.8 km / h;

5) 23.5 m / s = 23.5 ∙ 3600/1000 km / h = 23.5 ∙ 3.6 km / h = 84.6 km / h;

6) 30.4 m / s = 30.4 ∙ 3600/1000 km / h = 30.4 ∙ 3.6 km / h = 109.44 km / h.

If we take into account that 10 m / s = 36 km / h, you can faster to translate in km / h of magnitles, multiple 10:

20 m / s = 2 ∙ 10 m / s = 2 ∙ 36 km / h = 72 km / h;

30 m / s = 3 ∙ 10 m / s = 3 ∙ 36 km / h = 108 km / h;

50 m / s = 5 ∙ 10 m / s = 5 ∙ 36 km / h = 180 km / h.

Similar to values, multiple 5:

15 m / s = 3 ∙ 5 m / s = 3 ∙ 18 km / h = 54 km / h;

25 m / s = 5 ∙ 5 m / s = 5 ∙ 18 km / h = 90 km / h;

45 m / s = 9 ∙ 5 m / s = 9 ∙ 18 km / h = 162 km / h.