Question

the relationship between the net force acting on a body and its acceleration is it true? justify your answer don't copy from Google and I need long answer and its derivation too (spammers reported){ good writers brainlest answers}​

Answer 1

Answer:

F = ma

Explanation:

Yes but actually no, the relationship between Force and acceleration is true, also relation between force and mass is also true. It is famously known as Newton's Second Law of motion. And the relation is derived as follows :-

Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v. Here we see that, the initial momentum p1 :

$p_{1} = m*u$          [ m*u ]

The final momentum p2 :

$p_{2} =m*v$          [ m*v ]

As we know, the rate of change of momentum with respect to time is proportional to the applied force. i.e

$Force_{(net)}$ ∝ $\frac{Rate-of- change- of- Momentum}{Change-in- time}$     [that (=) sign is space between  

                                                                      two words cuz we can't put

                                                                      space in the equation using  

                                                                      brainly's tool ]    

So, the change in momentum can be written as :

$p_{2} -p_{1} = (m*v) - (m*u)$

            $= m*(v-u)$

Now the applied force will be :

$Force_{(net)}$ ∝ $\frac{ m*(v-u)}{t}$

Now as we know that  $\frac{(v-u)}{t}$ = a [Acceleration]

∴ F ∝ ma

Which is written as F = k × ma [where k is constant of proportionality]

and 'k' is taken as 1 or k = 1

Hence, F = ma

So your statement is half true and half false as The relationship between net force acting on a body and the product of mass and acceleration is true.

Hope it definitely helps.