Question

Acceleration is defined as the rate of change of velocity. Unit of rate of change of acceleration is:
$\left(A\right){\displaystyle \frac{m}{s^2}}$
$\left(B\right){\displaystyle \frac{m}{s^3}}$
$\left(C\right){\displaystyle \frac{m}{s}}$
$\left(D\right){\displaystyle \frac{m^2}{s^2}}$

Answer 1

Hint: In this question use the property that velocity is the ratio of distance to time and distance is measured in meter and time is measured in seconds later on in the solution use the property that rate of change of velocity is nothing but the differentiation of velocity w.r.t time so use these concepts to reach the solution of the question.

Complete step-by-step solution:

As we know that the velocity (V) is the ratio of distance (d) to time (t).
$\Rightarrow V={\displaystyle \frac{d}{t}}$
Now we all know that the unit of distance is meter and unit of time is sec.
So the unit of velocity (V) is m/s.
Now acceleration is known as rate of change of velocity.
As we see velocity is changing w.r.t. time so acceleration is also changing w.r.t. time.
Therefore acceleration (a) is the rate of change of velocity w.r.t. time (i.e. differentiation of the velocity w.r.t time)
$\Rightarrow a={\displaystyle \frac{dv}{dt}}$
So the unit of acceleration is ${\displaystyle \frac{{\displaystyle \frac{m}{s}}}{s}}={\displaystyle \frac{m}{s^2}}$
Now we have to find out the unit of the rate of change of acceleration.
So rate of change of acceleration w.r.t time (I.e. differentiation of acceleration) is given as
$\Rightarrow {\displaystyle \frac{da}{dt}}$
So the unit of rate of change of acceleration is $={\displaystyle \frac{\text{unit of acceleration}}{\text{unit of time}}}={\displaystyle \frac{{\displaystyle \frac{m}{s^2}}}{s}}={\displaystyle \frac{m}{s^3}}$
So this is the required answer.
Hence option (B) is the correct answer.

Note – Whenever we face such types of questions the key concept we have to remember is to always recall the unit of velocity and time so acceleration is the rate of change of velocity w.r.t. time we can easily calculate the unit of acceleration then use this unit to calculate the unit of rate of change of acceleration as above and simplify, we will get the required answer.