Question

Which law relates acceleration to mass?

Answer 1

We have to find the law which relates the acceleration of a body to its mass. Thus, we shall first look for the particular formula in physics which includes both the mass as well as acceleration of the body. Further, we shall analyze the three laws of motion given by Sir Isaac Newton especially the second law of motion.

Complete answer:
Newton’s First law tells us that an object at rest will stay at rest and an object with a constant velocity will keep having a constant velocity unless it is affected by some type of net force.
Now, the natural question is how a net force affects the constant velocity or state of an object. We shall find the answer to this question in Newton’s second law of motion.
According to Newton’s second law of motion, the force exerted on a body is equal to the mass of the body times its acceleration.
$\overrightarrow{F}=m\overrightarrow{.a}$
Where,
$\overrightarrow{F}=$ force exerted on the body
$m=$ mass of the body
$\overrightarrow{a}=$ acceleration of the body
$\Rightarrow \dfrac{\overrightarrow{F}}{m}=\overrightarrow{a}$
Thus, we see that for a constant force acting on the body, the acceleration of the body is inversely proportional to its mass.
$\Rightarrow \dfrac{1}{m}\propto \overrightarrow{a}$
Therefore, Newton’s second law of motion relates acceleration to mass.

Note:
Since force is a vector quantity, thus force exerted on a body can be both positive as well negative. The force acting on a moving body is said to be positive when the acceleration applied on the body is in the same direction as the motion of the body. However, the force acting on a body in motion is said to be negative when the acceleration of the body is in the opposite direction of the velocity of the body.