Question

The unit for the rate of change of velocity is:
\[A.\,\dfrac{m}{s}\]
\[B.\,\dfrac{m}{{{s}^{2}}}\]
\[C.\,Ns\]
\[D.\,\dfrac{N}{s}\]

Answer 1

Hint: The rate of change of the velocity is the acceleration. This is a direct question. There are two ways using which the question can be solved, that is, using the velocity formula we can solve this problem or, using the force formula we can solve this problem.

Formula used: \[a=\dfrac{dv}{dt}\]
\[F=ma\]

Complete step by step solution:
Using the definition of the acceleration, the unit for the rate of change of velocity can be solved as follows.
The rate of change of velocity is acceleration.
\[a=\dfrac{dv}{dt}\]
Again the rate of change of displacement is called the velocity.
\[a=\dfrac{d}{dt}\left( \dfrac{ds}{dt} \right)\]
\[\Rightarrow a=\dfrac{{{d}^{2}}s}{d{{t}^{2}}}\]
We know that the unit of the displacement is the meter and the unit of the time is time.
Thus, the unit of the acceleration is given as follows.
\[\Rightarrow a=\dfrac{m}{{{s}^{2}}}\] …… (1)
The acceleration is the ratio of the force by the mass.
\[a=\dfrac{F}{m}\]
Now we will substitute the units of the force and mass in the above equation to find the unit of the acceleration. So, we get,
The unit of the force is \[\dfrac{kg\,m}{{{s}^{2}}}\] and the unit of the mass is kg. substitute these units in the above equation. So, we get,
\[a=\dfrac{\dfrac{kg\,m}{{{s}^{2}}}}{kg}\]
Cancel out the common terms.
\[a=\dfrac{m}{{{s}^{2}}}\] …… (2)
The equations (1) and (2) represent the same unit of the rate of change of the velocity.

So, the correct answer is “Option B”.

Note: The options involve two types of units, one in terms of meter and seconds and the other in terms of Newton and seconds. Even, the option might involve the terms Newton and kg. 1 Newton equals kg per meter square.