Which physical quantity is represented by the first derivative of linear momentum with respect to time?

At any instant,the velocity of a particle of mass $500 \, g$ is $(2t \hat{i} + 3t^2 \hat{j}) \, ms^{-1}$. If the force acting on the particle at $t = 1 \, s$ is $(\hat{i} + x \hat{j}) \, N$,then the value of $x$ will be:

$A$ particle of mass $m$ at rest is acted upon by a force $P$ for a time $t$. Its kinetic energy after an interval $t$ is

State and explain Newton's second law of motion. Write its important points.

$A$ particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

$A$ force vector applied on a mass is represented as $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k} \, N$ and it accelerates with $1 \, m/s^2$. What will be the mass of the body?