Question

question - prove this f =ma????

Answer 1

Newton's 2nd law,.
Let Fnet and rate of change of momentum is 'delta p / delta t' ,then Fnet is directly proportional to 'delta p / delta t'.
Fnet =k*delta p / delta t. (k is proportionality constant)
The unit of force is so chosen that the value of constant k becomes 1.So that
Fnet = delta p / delta t .
We know that p=mv so, delta p = delta m*v.
lf the mass of the body is constant during its motion then delta p = m*delta v.
Therefore Fnet =m*delta v / delta t.
We know that delta v / delta t = a. (uniform acceleration)
Then Fnet = ma.

Answer 2

let us consider a body of mass M and initial velocity U and final velocity U in T seconds by a force F
according to second law of motion
force is directly proportional to the change in momentum
$f \: \alpha \: mv - mu \ \div t$
$f \alpha \: m(v \: - \: u) \: \div \: t \: \: \: \: \: \: \: \: \: \: \: (a)$
we know that
$a \: = v \: - \: u \: \div \: t \: \: \: \: \: \: \: \: \: \: \: (b)$
from a and b
$f \: \alpha \: ma$
$f = \: kma \: \: \: \: (k \: is \: consant \: of \: proportionality \: and \: here \: have \: a \: value \: of \: one$

$therefore \: \: \: \: \: \: \: \\ f = ma$