Question

A quantity has a value of $-16$ $m/{{s}^{2}}$. What does this quantity indicate ?

Answer 1

To identify the quantity asked in the question first look at its units.
The units of the quantity help to identify the quantity easily.In physics units are standards for measurement of physical quantities that need to be defined clearly. The units of the quantity may be described in SI units or CGS units or other units.

Complete answer:
We can also check the quantity by using dimensional analysis. In dimensional analysis we usually describe the quantity by its dimensions. In total there are seven fundamental dimensions or primary dimensions which are used to derive other dimensions called as derived dimensions or secondary dimensions.

The seven fundamental dimensions are: Mass (kilogram), Length (meter), Time(seconds), Electric Current (Ampere), Temperature (Kelvin), Amount of substance(mole), Luminous Intensity(candela). Here the unit is given as meter per second square ($m/{{s}^{2}}$). m means metre and s means second. Now using dimensional analysis we can say that it is acceleration.

Acceleration is the rate of change of velocity with respect to time.
$a=\dfrac{v}{t}$............where $a$ means acceleration, $v$ means velocity and $t$ means time.
Velocity is the rate of change of position with respect to time.
$v=\dfrac{s}{t}$...........where $v$ is velocity, $s$ is position and $t$ is time.
Now we can substitute the value of $v$ in $a=\dfrac{v}{t}$.
Now, $a=\dfrac{s}{{{t}^{2}}}$
Thus, acceleration is metre per second square.

The given quantity describes retardation of 16 $m/{{s}^{2}}$.

Note: Take care of plus minus sign as it describes the direction of the quantity. In case of acceleration minus sign indicates acceleration is acting in backward direction (Retardation).If the velocity of the body increases, acceleration is said to be positive.Similarly, if the velocity decreases, the acceleration is said to be negative.