Question

The rate of change of momentum is:
A. Velocity
B. Acceleration
C. Force
D. Impulse

Answer 1

Hint: In this question we have been asked to define what is the rate of change of momentum. We know that the rate of change of a quantity is taken as the ratio of quantity or the parameter over time. Therefore, we shall write the calculate the rate of change of momentum and select the appropriate answer from the given options. We also know that Newton's second Law deals with the rate of change of momentum. Therefore, we shall also discuss the second Law of Newton.

Formula used: $$P=mv$$
Where,
P is the momentum
m is the mass and
v is the velocity

Complete step by step answer:
Now, we have been asked to define the rate of change of momentum.
We know that momentum is given by,
$$P=mv$$
Therefore, rate of change of momentum say ‘F’ will be given by,
$$F={\displaystyle \frac{dP}{dt}}={\displaystyle \frac{d(mv)}{dt}}$$
Now, let us assume that over the period of time the mass remains constant.
Therefore, rate of change of momentum is given by,
$$F=m{\displaystyle \frac{dv}{dt}}$$
Now, the above equation gives a product of mass and rate of change of velocity. We know that the rate of change of velocity is acceleration.
We know,
$${\displaystyle \frac{dv}{dt}}=a$$
Therefore, we get,
$$F=ma$$
We know that mass times acceleration is given as force.
Also, the above equation proves Newton's Second law, which states that rate of change of momentum is known as force.

So, the correct answer is “Option C”.

Note: The foundation of classical mechanics was done by Sir Isaac Newton when he introduced the laws of motion. The laws of motion describe the relationship between mass of a body and the forces acting on it. And also, the reaction of objects to these forces. Newton postulated three different laws to describe the motion of a particle.