Question

Please derive 1 newtons law of motion quick

Answer 1

Newton's 2nd law of motion : The law states that the rate of change of momentum of a body is proportonal to the Force producing it and takes place in the direction in which the force acts. Momentum of a body = P = mass* velocity = mV (Vector quantity) ; V = Velocity Let m = mass of the body Initial velocity = u ; initial momentum = mu (Vector) Final velocity = v ; final velocity = mv (vector) Time interval = t Change in velocity = m(v - u) (vector) Rate of change of momementum = m(v - u) / t = m{(v- u)/t} = ma (vector) ; a = acceleration (vector) Instantaneous rate of change of momentum = dP/dt = (d/dt)(mV) = m(dV/dt) = ma Let the force acting on the body be F (vector) According to the 2nd law : F proportional to ma => F = k ma, (a vector equation), where k = constant ........ (1) Thus the directions of the Acceleration and the Force producing it are the same. Let us define Unit Force (Newton) as that force which when acts on a body of Unit Mass (1 kg) produces Unit Acceleration (1 m/s²). This means, Unit Force = k (Unit Mass)*(Unit Acceleration) => k = 1 Hence F = ma (a vector equation)