Question

State Newton's 2 law of motion and derive it mathematically

Answer 1

f

$= ma$

force is directly proportional to mass and acceleration

Answer 2

it states that change of momentum of a body is directly proportional to the external force applied on the body and the change takes place in the direction of the applied force.

let F be the external force applied on the body in the direction of motion of the body in the direction of motion of the body of mass m changes from v to v+Δv, .i.e change in momentum Δp = mΔv

according to newton's second law,

F∝Δp/Δt

or F=kΔp/Δt

where k is a constant of proportionality,

if limit is Δt→ o then Δp/Δt becomes the derivative dp/dt

thus, F = kdp/dt

for a body of fixed mass m, we have

F = k d(mv)/dt = km dv/dt

F = ma                                          ( dv/dt = a)

let k=1

then force F = ma

in scalar form it can be written as F = ma

∴1 unit force = 1 unit mass × 1 unit accelaration