What Is Metric Speed Formula and How to Solve Problems
Metric Speed
How do you find how fast an object is moving? Measured as distance travelled per unit of time, metric speed is the speed in meters per second (m/s). Thus, the SI derived unit for speed is meter per second. That said, a metric speed is described as the rate at which an object is moving (covering a specific distance). It is referred to as a scalar quantity as it only describes the magnitude and not direction. Do not confuse speed with velocity.
Formula of Speed
Speed = Distance traveled / Time taken
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Introduction To Velocity
Velocity is described as the rate of change of an object’s position in reference to a frame of time. Velocity falls under the category of a vector quantity as it defines both the magnitude as well as direction. The international system of unit (SI) derived unit for velocity is also meter per second (m/s) alike speed.
Formula of Velocity
Velocity= Change in position / Change in time
Introduction To Acceleration
Acceleration too falls under the classification of a vector quantity as it is described as the rate of change of velocity with reference to change in time.
The SI derived unit for acceleration is meter per square seconds (m/s2).
What is Speed in Meters Per Second (m/s)?
Speed in meters per second (m/s)
If an object is travelling at a speed of 1 m/s, it moves 1 meter every second.
1 m/s is like a very normal walking speed.
One hour of gentle walking at 1 m/s moves you about 3.6 km.
What Is Speed In Kilometers Per Hour (km/h)?
If an object is travelling at a metric speed of 2 km/h, it moves 2 kilometres every hour.
It is quite a slow walking speed. A kilometre per hour (km/h) is often used to express speed for a car.
Example: Highway speed of a car is around 150 km/h
One hour at this speed moves you 150 km.
Metric Speed Conversion
In this section, you will learn how to perform metric speed conversion using various formulae for the conversion. These formulae for the conversion consider values between different unit representations for speed/velocity.
Usually, the technique used to arrive at the formula is dependent upon the individual units inserted in the numerator and the denominator.
Unit Conversion For Meter/Second To kilometer/Hour (m/s to km/h)
M/s = ÷1,000km / ÷ 3,600 hour
M/s → × 3.6 → km/h
Unit Conversion For Kilometer/Hour To Meter/Second (km/h to m/s)
Km/hr = × 1000km / × 3600 hour
km/hr → × 0.28 → m/s
Unit Conversion For Kilometer/Second To Miles/Hour (km/s to mi/h)
Km/s = × 0.62137 mi / × 3600 hour
Km/s → × 2236.9 → mi/hr
Unit Conversion For Feet/Second To Meter/Second (ft/s to m/s)
Ft/s = × .3048 m/ × 1 s
Ft/s → × .3048 → m/s
Unit Conversion For Miles/Hour To Meter/Second (mi/h to m/s)
Mi/hr = × 1609.34 m / × 3600 hour
Mi/hr → × 0.447→ m/s
Unit Conversion For Meter/Second To Feet/Second (m/s to ft/s)
m/s = × 3.28084 ft / × 1 s
m/s → × 3.28→ ft/s
Unit Conversion For Kilometer/Second To Meter/Second (km/s to m/s)
km/s = ÷1000m / × 1 s
km/s → × 1000→ m/s
Unit Conversion For Feet/Minute To Meter/Second (ft/min to m/s)
ft/min = ×.3048m / × 60s
ft/min → ×.00508→ m/s
Unit Conversion For Miles/Hour To Feet/Second (mi/h to ft/s)
mi/hr = × 5280ft / × 3600s
mi/hr → ×1.47→ ft/s
Unit Conversion For Centimeter/Second To Meter/Second (cm/s to m/s)
cm/s = ÷100m / × 1s
cm/s → ÷100m → m/s
Unit Conversion For Rotations/Minute To Meter/Second
Rotation/min = × 2 Π× 2 r m / × 60 s
rpm → × 2 (Π× r/30) → m/s
Here,
r = radius
2 × π × r = Linear Velocity
Unit Conversion For Radians/Second To Meter/Second (rad/s to m/s)
Radian/sec = × r m / × 1 s
rad/s → × r → m/s
Unit Conversion For Meter/Second To Mach (m/s to Mach)
Mach refers to the ratio of the speed of a moving object through a fluid to the speed of sound via the same medium. because it is a ratio, it does not contain any dimension. The speed of the sound does not remain constant. It differs depending upon the temperature and atmospheric pressure.
m/s → × .0029104→ Mach
Solved Examples
Example: Convert a speed of a moving object 70 meters per second to kilometer per hour
Solution: For metric speed conversion of m/s to km/hr, we need to multiply it by 3.6
Thus, 70 m/s = 70 × 3.6 = 252 km/hr
Example: Convert a speed of of a car 20 feet per second (ft/s) to meters per second (m/s)
Solution:
Converting value from ft/s to m/s, we would require multiplying it by 0.3048
Thus, 20 ft/s = 20 × 0.3048 = 6.096 m/s
Conclusion: Metric speed helped you learn about the Speed,Time, Velocity and Acceleration, their definitions, units and the metric conversion, rules/formulae between different units. Thus, this may serve as a quick guide for any of the aforementioned concepts.
FAQs on Metric Speed in Maths with Clear Explanation
1. What is metric speed in maths?
Metric speed is the distance travelled per unit time measured using metric units such as metres and kilometres. In the metric system, speed is commonly expressed as:
- metres per second (m/s)
- kilometres per hour (km/h)
It tells us how fast an object is moving by comparing the distance covered to the time taken.
2. What is the formula for speed in the metric system?
The formula for speed is Speed = Distance ÷ Time. In symbols:
- S = D ÷ T
Where distance is measured in metres or kilometres and time is measured in seconds or hours. For example, if a car travels 120 km in 2 hours, its speed is 120 ÷ 2 = 60 km/h.
3. How do you calculate speed in metres per second?
To calculate speed in metres per second, divide the distance in metres by the time in seconds. Use the formula S = D ÷ T.
- Distance = 100 metres
- Time = 20 seconds
- Speed = 100 ÷ 20 = 5 m/s
Make sure both distance and time are in metric units (metres and seconds).
4. How do you convert km/h to m/s?
To convert kilometres per hour to metres per second, multiply by 5/18. The conversion formula is:
- m/s = km/h × 5/18
For example, 72 km/h = 72 × 5/18 = 20 m/s. This works because 1 km = 1000 m and 1 hour = 3600 seconds.
5. How do you convert m/s to km/h?
To convert metres per second to kilometres per hour, multiply by 18/5 (or 3.6). The formula is:
- km/h = m/s × 18/5
For example, 10 m/s = 10 × 18/5 = 36 km/h. This is a common metric speed conversion in maths problems.
6. What is the difference between speed and velocity in the metric system?
Speed is a scalar quantity that shows how fast something moves, while velocity is a vector quantity that includes both speed and direction.
- Speed example: 50 km/h
- Velocity example: 50 km/h north
Both can be measured in m/s or km/h, but only velocity includes direction.
7. How do you find distance using speed and time?
Distance is calculated using the formula Distance = Speed × Time. In symbols:
- D = S × T
For example, if a cyclist travels at 15 km/h for 3 hours, the distance covered is 15 × 3 = 45 km.
8. How do you find time when speed and distance are given?
Time is calculated using the formula Time = Distance ÷ Speed. In symbols:
- T = D ÷ S
For example, if a train travels 150 km at 75 km/h, the time taken is 150 ÷ 75 = 2 hours.
9. What are common units of speed in the metric system?
The most common metric units of speed are metres per second (m/s) and kilometres per hour (km/h).
- m/s is commonly used in physics and science.
- km/h is commonly used for vehicles and road speed limits.
Both units measure how much distance is covered in a given time.
10. What are common mistakes when solving metric speed problems?
The most common mistake in metric speed problems is mixing up units without converting them properly.
- Not converting hours to seconds when finding m/s
- Forgetting to use the correct formula (S = D ÷ T)
- Mixing kilometres with metres
Always ensure distance and time are in compatible metric units before applying the speed formula.
