Question

Derive expression for newton's second law ​

Answer 1

Explanation:

Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system. Force applied is directly proportional to the product of mass and acceleration . Let be the initial and final momentums respectively. ... F=kma.

Answer 2

Answer:

Ello❤

Newtons second law✴✴

Statement :

the rate of chnge of linear momentum of a body is directly proportional to the external force applied on the body,and this charge takes place always in the direction of the applied force

Derivation:

The law implies that when a bigger force is applied on a body of given mass ,its linear momentum will change in the direction of the applied force . To understand it

Further ,suppose

M= mass

V= velocity

P= linear momentum

P= mv........1

F= external force applied on a body

delta p = a small chnge in linear momentum of the body in a small time delta t

Rate of change of linear momentum of the body

=delta p/delta t

$acc \: to \: newtos \: second \: law \\ \frac{delta \: p}{delta \: t} \alpha f \\ f = k\frac{delta \: p}{delta \: t} \\ taking \: a \: limit \\ it \: becomes \frac{dp}{dt} \\ f = k \frac{dp}{dt} ........2 \\ substitute \: equn \: 1and \: 2 \\ f = k \frac{d}{dt} (mv) = km \frac{dv}{dt} \\ as \: \frac{dv}{dt} = a \\ \\ therefore \: f = kma........3$

The value of constant of proportion k depend on the units adopted for measuring the force . Both in SI and CGS system , the unit of force is selected in such a manner that k=1

substitute k in equn 3

Therefore,

F= ma

Hope its help u❤✴✴

THANKS❤