Answer :
To determine which of the options represents a unit of acceleration, we first need to understand what acceleration is and how it is measured.
Acceleration is defined as the rate of change of velocity with respect to time. In physics, the standard unit for velocity is meters per second ([tex]$m/s$[/tex]). Therefore, acceleration is the change in velocity per second, which means that it involves a change in [tex]$m/s$[/tex] over time. Consequently, to express acceleration mathematically, we use:
[tex]\[ \text{acceleration} = \frac{\text{change in velocity}}{\text{time}} = \frac{m/s}{s} = m \cdot s^{-2} = \frac{m}{s^2} \][/tex]
Now, let's examine each of the provided options:
A. [tex]\( \frac{m}{s^2} \)[/tex]
- This matches our derived unit for acceleration (meters per second squared).
B. [tex]\( \frac{m^2}{s} \)[/tex]
- This represents an area per time, which is not a unit of acceleration.
C. [tex]\( \frac{m^2}{s^2} \)[/tex]
- This represents area change rate per second squared, not acceleration.
D. [tex]\( \frac{m}{s} \)[/tex]
- This represents velocity (meters per second), not acceleration.
From these evaluations, we can conclude that the correct unit for acceleration is:
A. [tex]\( \frac{m}{s^2} \)[/tex]
Thus, the correct choice is [tex]\( \boxed{A} \)[/tex].
Acceleration is defined as the rate of change of velocity with respect to time. In physics, the standard unit for velocity is meters per second ([tex]$m/s$[/tex]). Therefore, acceleration is the change in velocity per second, which means that it involves a change in [tex]$m/s$[/tex] over time. Consequently, to express acceleration mathematically, we use:
[tex]\[ \text{acceleration} = \frac{\text{change in velocity}}{\text{time}} = \frac{m/s}{s} = m \cdot s^{-2} = \frac{m}{s^2} \][/tex]
Now, let's examine each of the provided options:
A. [tex]\( \frac{m}{s^2} \)[/tex]
- This matches our derived unit for acceleration (meters per second squared).
B. [tex]\( \frac{m^2}{s} \)[/tex]
- This represents an area per time, which is not a unit of acceleration.
C. [tex]\( \frac{m^2}{s^2} \)[/tex]
- This represents area change rate per second squared, not acceleration.
D. [tex]\( \frac{m}{s} \)[/tex]
- This represents velocity (meters per second), not acceleration.
From these evaluations, we can conclude that the correct unit for acceleration is:
A. [tex]\( \frac{m}{s^2} \)[/tex]
Thus, the correct choice is [tex]\( \boxed{A} \)[/tex].
