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Question: The SI unit of retardation is: A.)\(\dfrac{m}{{{s}^{2}}}\) B.)\(\dfrac{m}{s}\) C.)\({{m}^{2}...

The SI unit of retardation is:
A.)ms2\dfrac{m}{{{s}^{2}}}
B.)ms\dfrac{m}{s}
C.)m2{{m}^{2}}
D.)s2{{s}^{2}}

Explanation

Solution

Hint : Convert the mathematical formula of retardation into basic measurement units in the SI system. Retardation is negative acceleration. It is retardation which increases with decreasing velocity of body unlike acceleration.

Formulae used: The basic formulae derived from the definition of acceleration and velocity are used. i.e. acceleration=change in velocitychange in time\text{acceleration}=\dfrac{\text{change in velocity}}{\text{change in time}} and velocity=change in displacementchange in time\text{velocity}=\dfrac{\text{change in displacement}}{\text{change in time}}

Complete answer step by step:
The International System of Units (SI) was introduced to standardize the measurement units across every system and place. For example, if a quantity is measured somewhere then, all around the world the interpretation should be the same. This system promises uniformity in measurements. There are seven base units of measurements.

Second (s): unit of time
Meter (m): unit of time length
Kilogram (kg): unit of time mass
Ampere (A): unit of time electric current
Kelvin (K): unit of thermodynamic temperature
Mole (mol): unit of amount of substance
Candela (s): unit of luminous intensity

Retardation for an object is defined as the rate of change of the velocity with respect to time. Whereas, the velocity is defined as the rate of change in its displacement with respect to time.

The equation for acceleration is:

acceleration=change in velocitychange in time\text{acceleration}=\dfrac{\text{change in velocity}}{\text{change in time}}

Similarly, the equation for velocity looks like,

velocity=change in displacementchange in time\text{velocity}=\dfrac{\text{change in displacement}}{\text{change in time}}
We know, displacement is a measurement of length, with SI unit mm, and time has SI unit ss. Therefore, Substituting the SI units in the equation of velocity, we get the SI unit of velocity as ms\dfrac{m}{s} .

Now, we substitute this SI unit of velocity into the equation of acceleration. To obtain
mss=ms2\dfrac{\dfrac{m}{s}}{s}=\dfrac{m}{{{s}^{2}}}
Which means the SI unit of retardation is option A. ms2\dfrac{m}{{{s}^{2}}} .

Note : Retardation and acceleration essentially determine the same quantity for an object in motion. Retardation is the decrement in the value of velocity per unit time. Since it is a measure of decrement, retardation is positive for a negative acceleration. Whereas, it is negative when the acceleration is positive.