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What is the relation between force and acceleration?

Last updated date: 23rd May 2024
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Hint: With the help of Newton’s second law we can find the relation between force and acceleration. In general we can feel how much force you applied on any object that much the body gains velocity means if we applied large force then change in velocity is high it can gain higher velocity in less time and as we know acceleration is change in velocity per unit time. so we can relate force and acceleration .

Complete step by step solution:
As we know the Newton’s second law of motion which states that the rate of change of momentum is equal to the applied force
According to second law force
$F = \dfrac{{dp}}{{dt}}$
Here $F$ applied force on the body
$dp$ Change in momentum of the body in small time $dt$
$ \Rightarrow F = \dfrac{{dp}}{{dt}}$
We know momentum $p = mv$
Here $m$ is the mass of body and $v$ is the velocity of body
Put the value p momentum in above equation
$ \Rightarrow F = m\dfrac{{dv}}{{dt}}$
$m$ Is constant for a body
We know the rate of change of velocity is known as acceleration
$a = \dfrac{{dv}}{{dt}}$
From above equation
$ \Rightarrow F = ma$
This is known as another form of Newton’s second law of motion.

From this we can clearly see that the force is directly proportional to the applied force.

Note: Newton’s second law of motion can be formally stated as follows: the acceleration of an object is directly proportional to the magnitude of the net force and inversely proportional to the mass of the object. If we apply a large force on a body then it gains its velocity with large acceleration.