Question

derive the relation between force and acceleration.

Answer 1

Newton’s second law of motion states that the force exerted by a body is directly proportional to the rate of change of its momentum.

For a body of mass ‘m’, whose velocity changes from u to v in time t, when force ‘F’ is applied, then we have

$F\propto \frac{dp}{dt}$

$F\propto \frac{d\left(mv\right)}{dt}$ (Since $p=mv$)

$F\propto m\frac{dv}{dt}$

$F\propto ma$ (Since $\frac{dv}{dt}=a$)

$\Rightarrow F=kma$

$\Rightarrow F=ma$ (Since $k=constant=1$).