Question

The SI unit of acceleration is m/s. State whether this statement is True or False.

Answer 1

Hint- Here, we will proceed by defining the term acceleration which is extensively used in physics. Then, we will give a mathematical equation to find the acceleration and from there we will determine the SI units of acceleration.
Formula Used- $\overrightarrow a = \dfrac{{\overrightarrow {{v_2}} - \overrightarrow {{v_1}} }}{{{t_2} - {t_1}}}$

Complete Step-by-Step solution:
Acceleration is defined to be the rate of change of the velocity with respect to time.
If ${v_1}$ is the initial velocity of an object at time ${t_1}$ and ${v_2}$ is the final velocity of the object at time ${t_2}$. Then, the acceleration of the object is given by
$a = \dfrac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}}{\text{ }} \to (1{\text{)}}$
Since, the velocity of any object is a vector quantity so that acceleration of any object will also be vector quantity. Any vector quantity has both direction and magnitude whereas any scalar quantity has only magnitude. In order to represent any vector quantity, both magnitude and direction are needed.
In vector form, the acceleration can be written as
$\overrightarrow a = \dfrac{{\overrightarrow {{v_2}} - \overrightarrow {{v_1}} }}{{{t_2} - {t_1}}}$
The SI unit of time is second and the SI unit of velocity is metre per second (m/s) which is the same as those of speed. The only difference between velocity and speed is that the speed is the magnitude of the velocity vector quantity (i.e., speed is a scalar quantity).
The SI unit of acceleration according to the formula mentioned in equation (1) will be given by
SI unit of acceleration = $\dfrac{{{\text{SI unit of velocity}}}}{{{\text{SI unit of time}}}} = \dfrac{{\left( {\dfrac{{\text{m}}}{{\text{s}}}} \right)}}{{\text{s}}} = \dfrac{{\text{m}}}{{{\text{s}} \times {\text{s}}}} = \dfrac{{\text{m}}}{{{{\text{s}}^2}}}$
Clearly, from the above equation we can say that the SI unit of acceleration is metre per square seconds (i.e., m/${{\text{s}}^2}$).
Therefore, the SI unit of acceleration is not metre per second (m/s).
Hence, the given statement is False.

Note- In this particular problem, we have mentioned that the SI units of velocity is metre per second (i.e., m/s). This is because velocity is defined as the rate of change of position with respect to time (i.e., displacement per unit time) where displacement is simply length (having SI unit as metre) and the SI unit of time is second.