[Maths Class Notes] on Metric Speed Pdf for Exam

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

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.