Question

How to measure the rate of change of momentum with time?

Answer 1

In the question, we asked how to measure the rate of change of momentum with time. As a first step, you could define momentum to begin with. Then recall the second law of motion and substitute for acceleration as the time rate of change of velocity and thus find the answer.

Formula used:
Momentum,
$P=mv$
Newton’s second law,
$F=ma$

Complete step-by-step solution:
In the question, we are asked to find how to measure the rate of change of momentum with time.
Let us first recall what exactly is momentum. Momentum is known to be the product of mass and velocity by definition. Mathematically, momentum P would be given by,
$P=mv$……………………………………… (1)
Momentum is known to be the concept that could explain some of the most important interactions in nature.
Now, let us discuss force. When a force is known to act on an object, that object undergoes a change in momentum.
We know from Newton’s second law of motion, force is given by the product of mass and acceleration. That is,
$F=ma$
Also, acceleration is defined to be the time rate of change of velocity, so,
$a=\dfrac{v}{t}$
$\Rightarrow F=m\dfrac{v}{t}$…………………………… (2)
From (1) and (2) we get,
$F=\dfrac{P}{t}$
So, if we could find the force acting on a body, we are basically finding the time rate of change of momentum of that body.

Note: While measuring any physical quantity, its unit plays a very important role. Force is measured in Newtons(N) which is also its SI unit. Now we could measure change in momentum in units of kilogram metres per second (kg m/s) and the time taken is measured in units of seconds(s).