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# Complete the following:Force = mass $\times$ _______

Last updated date: 20th Jun 2024
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Hint: Use Newton's second law of motion which is a quantitative description of the changes that a force can produce on the motion of a body. This gives us the required term in the blank.

Complete step by step solution:
Newton’s second law states that time rate of change of momentum of a body is equal in both magnitude and direction to the force imposed on it i.e.
$\overrightarrow{F}=\dfrac{d\overrightarrow{p}}{dt}$
Where $\overrightarrow{F}$ is the force
$\dfrac{d\overrightarrow{p}}{dt}$ Is the time rate of change in momentum
The momentum of a body is equal to the product of its mass and its velocity. Momentum like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum, or its direction, or both.
$\overrightarrow{p}=m\overrightarrow{v}$
$\dfrac{d\overrightarrow{p}}{dt}=\dfrac{d}{dt}\left( m\overrightarrow{v} \right)$
Taking mass of the body to be constant,
$\dfrac{d\overrightarrow{p}}{dt}=m\dfrac{d\overrightarrow{v}}{dt}$
As we know that the time rate of change of velocity is the acceleration of the body.
So,
$\dfrac{d\overrightarrow{p}}{dt}=m\overrightarrow{a}$
$\therefore ,\text{ }\overrightarrow{F}=m\overrightarrow{a}$
Or
Force = mass $\times$ acceleration
Here, force and acceleration are both vector quantities. If a body has a net force acting on it, it is accelerated in accordance with the equation. Conversely, if a body is not accelerated, there is no net force acting on it.

Note:
Remember that this relation is only good for objects that have constant mass. This equation tells us that an object subjected to an external force will accelerate and that amount of acceleration is proportional to the size of the force. The amount of acceleration is also inversely proportional to the mass of the object; for equal forces, a heavier object will experience less acceleration than a lighter object.
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