Question

What are the S.I units of acceleration?

Answer 1

Hint: Here, we will proceed by defining the term acceleration used in physics. Then, we will give the mathematical formula for acceleration in which we will substitute the S.I units of all the quantities (expect acceleration).
Formula Used- ${\text{a}} = \dfrac{{d{\text{v}}}}{{dt}}$.

Complete Step-by-Step solution:
Acceleration of a body is defined as the rate of change of velocity of the body with respect to time. If no acceleration is acting on a body this means that the body will be moving with a constant velocity or uniform velocity.
Mathematically, acceleration acting on the body is given by
${\text{a}} = \dfrac{{d{\text{v}}}}{{dt}}$ where v denotes the velocity of the body and t represents the time
In the above equation, dv represents the small change in velocity and dt represents the small change in time
As we know that the S.I unit of velocity is metre per second (m/s) and that of time is second (s). So, the S.I unit of small change in velocity i.e., dv will be same as that of velocity and the S.I unit of small change in time i.e., dt will be same as that of time
So, S.I unit of dv = metre per second (m/s)
S.I unit of dt = second (s)
Using equation (1), we can write
S.I unit of acceleration = $\dfrac{{{\text{S}}{\text{.I unit of dv}}}}{{{\text{S}}{\text{.I unit of dt}}}}$
$ \Rightarrow $ S.I unit of acceleration = $\dfrac{{{\text{metre per second}}}}{{{\text{second}}}} = \dfrac{{{\text{metre}}}}{{{{\left( {\operatorname{second} } \right)}^2}}}$
Therefore, the S.I units of acceleration is metre per square second i.e., m/${{\text{s}}^2}$.

Note- Velocity of a body is simply defined as the rate of change of position of the body with respect to time i.e., v = $\dfrac{{dx}}{{dt}}$ where x denotes the position of the body. As, we know that the S.I unit of position is the same as the S.I unit of distance which is metre (m) and S.I unit of time is second (s). That’s why the S.I unit of velocity is m/s.