Unit of Speed: SI Unit, CGS Unit, Conversion & Speed Formula

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Muskan Shafi

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Unit of Speed is ‘meters per second’ (m/s). Speed is the rate of change in distance with time. SI unit of Speed is the combination of the standard units of distance and time. The unit of distance is meter (m) and the unit of time is second (s), thus, the SI unit of speed is meters per second (m/s).

  • Speed is the distance covered by an object per unit of time.
  • It is the ratio of the distance covered by the total time taken to cover that distance.
  • Speed is a scalar quantity as it only has direction and no magnitude.
  • The SI Unit of Speed is denoted as m/s or m.s-1.
  • Other units of speed are kilometers per hour, feet per second, miles per hour, etc.
  • Speed is calculated using the formula: Speed = Distance/Time

Read More: Measurement of Speed

Key Terms: Speed, SI Unit of Speed, Speed Formula, Distance, Time, Scalar, CGS Unit, Meters per Second, Magnitude, Unit Conversion


What is Speed?

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Speed is the rate of change of position of an object moving in any direction.

  • Speed is the ratio of the distance covered by an object to the time in which the distance was covered.
  • It is a scalar quantity, with only magnitude and no associated direction.

Dimensional Analysis Video Explanation

Speed is the measurement of how fast an object moves to cover a distance.

  • Speed can not have a negative value.
  • The dimensional formula of Speed is M0.L1.T-1
  • It is denoted by the symbol v and is measured in the units of meters per second (m/s).

Speed

Interesting Facts about Speed

  • Galileo Galilei, a great Italian astronomer was the first to estimate speed by calculating distance over time.
  • Earth's typical orbital speed is around 30 km/s.
  • Earth's surface moves at a rate of around 460 m/s at the equator which is equal to a speed of around 1,000 miles per hour.
  • In a vacuum, the speed of light is approximately 299,792 kilometers per second (186,282 miles per second).
  • In the air, the speed of sound is approximately 343 m/s, or 767 mph, or 1235 km/h.

SI Unit of Speed

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SI Units are the standard units of measurement that are uniform throughout the world to avoid confusion. SI units of any physical quantity are laid out by the International System of Units (SI).

The SI Unit of Speed is Meters per Second (m/s). 
  • This standard unit of speed signifies how many meters an object can travel within a second.
  • For instance, if an object travels 10 meters in a second, then, the speed of the object will be 10 m/s.

The SI unit of speed is derived from the standard units of Distance (meters) and Time (seconds). It can be understood as follows:

\(Unit \hspace{1mm} of\hspace{1mm} Speed = \frac{Unit\hspace{1mm} of \hspace{1mm}Distance}{Unit \hspace{1mm}of \hspace{1mm}Time} = {m\over s}\)

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Other Units of Speed

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Speed can be measured in various other units apart from its SI unit. In certain cases such as measuring a vehicle's speed, it is more sensible to use hours instead of seconds. Thus, kilometers per hour (kmph) or miles per hour are used to measure the speed of vehicles.

The different systems of measurement of speed are:

  • CGS Unit of Speed: In the CGS system of units, length is measured in terms of centimeters and time in terms of seconds. Therefore we can derive the unit of speed as centimeters per second or cm/s.
  • FPS Unit of Speed: FPS Units belong to the category of imperial units. Here, length is measured in terms of foot and time in terms of the second. Therefore, the unit of speed can be expressed as a foot per second or ft/s.

Units of Speed

Read More: Difference Between Speed and Velocity


Conversion of Units of Speed

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The unit conversion of the different units of speed from CGS to SI system and vice versa can be done with the help of the given table:

Units Conversion
Km to Cm 1 km = 100000 cm
Km to M 1 km = 1000m
Cm to m 1 cm = 0.01m
M to mm 1 m = 1000 mm
Cm to mm 1cm = 10 mm
Hour to min 1 h = 60 min
Min to sec 1 min = 60 sec

Speed Formula

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Speed is the ratio of the distance covered by an object to the time taken to cover that distance. Speed can be calculated using the given formula:

\(Speed = {Distance \over Time}\)

Using the appropriate symbols for all the physical quantities, the Speed Formula is expressed as: 

\(v = {d \over t}\)

Where

  • d is the Distance covered by an object measured in meters (m).
  • t is the time taken to cover the distance measured in seconds (s).
  • v denotes the Speed of an Object measured in m/s.

Speed, Distance, and Time Formula

Speed, Distance, and Time Formula

Solved Example

Example: A train covers a distance of 120 km in an hour. What will be the speed of the train in m/s?

Solution: It is given that

  • Distance covered by Train = 120 km = 120 × 1000m = 120000m 
  • Time Taken by Train = 1 hour = 60 × 60 = 3600 second

Using the Speed Formula,
Speed = Distance/Time

Speed of Train = 120000/3600 = 33.3m/sec

Thus, the speed of the train is 33.3 m/s.

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Things to Remember 

  • Speed is the rate at which an object travels over a certain distance.
  • Speed is a scalar quantity with only direction and no magnitude.
  • It is measured in terms of distance divided by time.
  • Speed Formula is given as Speed = Distance/Time.
  • The SI unit of Speed is meters per second (m/s).
  • The CGS unit of speed is centimeters per second (cm/s).
  • The FPS unit of speed is foot per second (ft/s).
  • The speed of vehicles is always measured in terms of Kilometers per hour (kmph) or miles per hour (mph).

Previous Years’ Questions

  1. A block of mass of 1 kg is moving on the x-axis… [UPSEE 2017]
  2. If a body moves for 2 s with 15 m/s velocities towards the east and then moves… [JCECE 2006]
  3. A packet is dropped from a flight ascending with a velocity at a height of… [KEAM 2013]
  4. The position x of a particle with respect to time t along… [NEET 2007]
  5. The apparent frequency observed by a moving observer away from… [KEAM]
  6. The variation of speed (in m/s) of an object with time… [KEAM]
  7. The linear momentum p of a body varies with time and it is given by… 
  8. The velocity of an object moving in a straight line path is given as… 
  9. A child is swinging a swing. Minimum and maximum heights of swing from… [JCECE 2004]
  10. Hie equation of motion of a panicle is given by… [TS EAMCET 2018]
  11. The nature of a graph drawn for a freely falling body with time on… [TS EAMCET 2019]
  12. A body moving with uniform acceleration describes 40 m in the first… [COMEDK UGET 2004]
  13. The displacement time graph for two bodies A and B are straight lines… [COMEDK UGET 2004]
  14. What will be the ratio of speed in the first two seconds to the speed in the next… 
  15. If a person sitting in a train moving with a constant velocity along a straight line… 

Sample Questions

Ques. What is the SI Unit of Speed? (1 Mark)

Ans. The SI unit of Speed is meters per second (m/s). Speed is defined as the distance traveled per unit of time. Meter is the SI unit of distance, and the second is the SI unit of time, hence the SI unit of speed is m/s.

Ques. What is Speed? (1 Mark)

Ans. Speed is defined as the rate of change of distance with respect to time. It is the ratio of the distance covered by an object with respect to the time it takes to cover that distance. Speed is calculated using the given formula:

\(Speed = {Distance \over Time}\)

Ques. A car covers 20 km in 50 minutes. Find the speed of the car using the speed formula. (3 Marks)

Ans. Given that,

  • Distance covered by Car = 20 km = 20×1000 = 20000 m 
  • Time Taken = 50 minutes = 50×60 = 3000 second

Using the Speed Formula, 
Speed = Distance/Time 

Speed of Car = 20000/3000 = 6.67m/s

Thus, the speed of the car is 6.67m/s.

Ques. What is the unit of speed of light? (1 Mark)

Ans. The units used to express the speed of light are the same as those used to express the speed of normal objects. The SI unit of speed is m/sec, although one may use miles per hour or any other speed unit.

Ques. Convert 60 km/h into m/sec. (2 Marks)

Ans. Given speed is 60 km/h.

  • 1 km = 1000m
  • 1 hour = 3600 seconds.

On conversion of the speed, we get

60 x 5/18 

16.66 m/sec

Ques. What are the types of Speed? (2 Marks)

Ans. There are four main types of Speed which are as follows:

  • Uniform Speed
  • Variable Speed
  • Average Speed
  • Instantaneous Speed

Ques. Convert 150 m/s to km/h. (2 Marks)

Ans. Given speed is 150 m/s.

  • 1 m = 1/1000 km
  • 1 second = 1/3600 hours

On simplification, we get

150x 18/5 

540 km/h

Ques. What do you mean by Uniform Speed? (1 Mark)

Ans. If an object covers an equal distance in an equal interval of time, then the object is said to be moving with a uniform speed. An example of uniform speed will be a body sliding on a frictionless surface with a constant speed.

Ques. Determine which is a higher speed:155 km/h or 75 m/s. (2 Marks)

Ans. To compare, we need to first convert 75 m/s into km/h.

Converting 75 m/s into km/h, we get

75 * 18/5 

270 km/h

Now, between 155 km/h and 270 km/h, 270 km/h is a higher speed, because the distance covered in an hour is more than 155 km/h.

Ques. An object has moved through a distance. Can it have a zero displacement? If yes, support the answer with an example. (1 Mark)

Ans. Yes, the object in spite of moving through a distance can have a zero displacement. For example, if an object travels from point ‘A’ and reaches the same point ‘A’, then its displacement is zero as the initial and final positions of the object are the same.

Ques. Distinguish between speed and velocity. (2 Marks)

Ans. The difference between speed and velocity is as follows:

Velocity Speed
Velocity is the rate at which an object changes position in a particular direction. Speed is the rate at which an object covers a certain distance per unit of time.
Velocity is a vector quantity as it has direction. Speed is a scalar quantity as it does not have direction.
The velocity of an object can be zero, negative, or positive. The speed of an object can never be negative or zero.

Ques. It took 2s after lightning for the sound of thunder to reach a person. How far did the lightning strike? The speed of sound is 346 m/s in air. (3 Marks)

Ans. The speed of sound is 346 m/s in air.

  • Time Given: 2s
  • Distance Covered:?

We know that,

Speed = Distance/Time

  • Distance = Speed x Time
  • Distance = 346 x 2 = 692 m

Thus, the lightning struck 692 m away from the person.


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CBSE CLASS XII Related Questions

1.

A series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80mF, R = 40 Ω.

(a) Determine the source frequency which drives the circuit in resonance.

(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.

(c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency

      2.
      A series LCR circuit with R = 20 W, L = 1.5 H and C = 35 μF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

          3.
          (a) A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of 60° with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning. 
          (b) Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

              4.
              Check that the ratio \(\frac{ke^2}{ Gm_e m_p}\) is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

                  5.
                  A closely wound solenoid of \(2000 \) turns and area of cross-section \(1.6 × 10^{-4}\  m^2\), carrying a current of \(4.0 \ A\), is suspended through its centre allowing it to turn in a horizontal plane. 
                  (a) What is the magnetic moment associated with the solenoid?
                  (b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of \(7.5 × 10^{-2}\  T\) is set up at an angle of \(30º\) with the axis of the solenoid?

                      6.
                      A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field ?
                      1. inside the sphere
                      2. just outside the sphere
                      3. at a point 18 cm from the centre of the sphere?

                          CBSE CLASS XII Previous Year Papers

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