Question

state and prove Newton's second law of motion​

Answer 1

$\: \: \: \: \large\bold{\underline{\underline{\blue{Newton's \: second \: law \: of \: motion}}}}$

Defining Newton’s Second Law of Motion

Newton’s second law states that the acceleration of an object depends upon two variables – the net force acting on the object and the mass of the object. The acceleration of the body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body. This means that as the force acting upon an object is increased, the acceleration of the object is increased. Likewise, as the mass of an object is increased, the acceleration of the object is decreased.

Newton’s second law can be formally stated as,

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This statement is expressed in equation form as,

$\: a= \frac{Fnet}{m}$

The above equation can be rearranged to a familiar form as

$\fcolorbox{black}{white}{F=ma}$

Since force is a vector, Newton’s second law can be written as

$\fcolorbox{black}{white}{F⃗ =ma⃗ }$

The equation shows that the direction of the total acceleration vector points in the same direction as the net force vector.