How to Calculate and Convert Metric Speed in Maths
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 Explained: Formula, Conversion & Examples
1. What is meant by 'metric speed' in simple terms?
Metric speed is a measure of how fast an object is moving, calculated using units from the metric system. The most common units are metres per second (m/s) and kilometres per hour (km/h). It is calculated by dividing the distance travelled (in metres or kilometres) by the time taken (in seconds or hours).
2. What is the primary difference between speed and velocity when using metric units?
The primary difference lies in direction. Speed is a scalar quantity, meaning it only describes how fast an object is moving (e.g., 50 km/h). Velocity is a vector quantity, meaning it describes both how fast the object is moving and in what direction (e.g., 50 km/h North). While both use the same metric units, velocity includes directional information.
3. How do you calculate speed using the metric system formula?
To calculate speed using the metric system, you use the formula: Speed = Distance / Time. For it to be a metric speed calculation, the units must be from the metric system. For example:
- If distance is in metres (m) and time is in seconds (s), speed will be in m/s.
- If distance is in kilometres (km) and time is in hours (h), speed will be in km/h.
4. Can you provide a real-world example of calculating metric speed?
Certainly. Imagine a cyclist travels a distance of 30 kilometres in 2 hours. To find their average speed in metric units, you would use the formula:
Speed = Distance / Time
Speed = 30 km / 2 h
Speed = 15 km/h.
This means the cyclist covered an average distance of 15 kilometres for every hour of travel.
5. How are SI units related to the measurement of metric speed?
The metric system is fundamentally based on the International System of Units (SI). For speed, the base SI unit for distance is the metre (m) and for time is the second (s). Therefore, the official SI unit for speed is metres per second (m/s). While kilometres per hour (km/h) is also a metric unit, m/s is the standard used in scientific calculations and formulas.
6. Why is the metric system (km/h) generally preferred over the imperial system (mph) in science?
The metric system is preferred in science and by most countries for several reasons:
- Simplicity: It is a base-10 system, which makes conversions between units straightforward (e.g., 1 km = 1000 m).
- Standardisation: It provides a universal standard, which is crucial for international scientific collaboration and avoiding conversion errors.
- Coherence: Metric units for distance, mass, and volume are logically interconnected, making complex calculations more intuitive than in the imperial system.
7. How can you convert a speed from kilometres per hour (km/h) to metres per second (m/s)?
To convert km/h to m/s, you can use the shortcut of multiplying the speed by 5/18. This factor is derived from the base conversions: 1 km = 1000 metres, and 1 hour = 3600 seconds. For example, to convert 72 km/h to m/s:
72 km/h = 72 × (1000 m / 3600 s) = 72 × (5/18) m/s = 20 m/s. This shows that a speed of 72 km/h is equivalent to travelling 20 metres every second.
8. What is a common mistake when converting between metric speed units like m/s and km/h?
A very common mistake is reversing the conversion factor. Students often mix up when to multiply by 5/18 and when to multiply by 18/5. A simple way to remember is:
- When going from a larger unit to a smaller unit (km/h to m/s), use the smaller fraction (5/18).
- When going from a smaller unit to a larger unit (m/s to km/h), use the larger fraction (18/5).
