The engine of a jet aircraft applies a thrust force of $10^5\, N$ during take-off and causes the plane to attain a velocity of $1\, km/s$ in $10\, s$. The mass of the plane is:

$A$ particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F = F_{0} \left(1 - \left(\frac{t - T}{T}\right)^{2}\right)$. Where $F_{0}$ and $T$ are constants. The force acts only for the time interval $2T$. The velocity $v$ of the particle after time $2T$ is:

The velocity $(v)$ of a particle (under a force $F$) depends on its distance $(x)$ from the origin (with $x > 0$) as $v \propto \frac{1}{\sqrt{x}}$. Find how the magnitude of the force $(F)$ on the particle depends on $x$.

When $1\,N$ force acts on a $1\,kg$ body that is able to move freely,the body receives:

If the mass and the acceleration of an object are both doubled,how does the force acting on the object change with respect to its previous value?

State Newton's second law of motion.