$A$ 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?

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

The motion of a particle of mass $m$ is described by $y = ut + \frac{1}{2}gt^2$. Find the force acting on the particle.

$A$ constant force acting on a body of mass $5\,kg$ changes its speed from $5\,ms^{-1}$ to $10\,ms^{-1}$ in $10\,s$ without changing the direction of motion. The force acting on the body is ......... $N$.

$A$ force acting on a body of mass $5 \ kg$ is $(4 \hat{i} - 2 \hat{j} + 3 \hat{k}) \ N$. If the body is initially at rest,then the magnitude of its velocity at the end of $10 \ s$ in $m/s$ will be:

$A$ particle of mass $2/3 \, kg$ with velocity $v = -15 \, m/s$ at $t = -2 \, s$ is acted upon by a force $F = k - \beta t^2$. Here,$k = 8 \, N$ and $\beta = 2 \, N/s^2$. The motion is one-dimensional. Then,the speed at which the particle acceleration is zero again,is ........... $m/s$.