$A$ body of mass $2\, kg$ travels according to the law $x = at + bt^2 + ct^3$,where $a = 3\, m/s$,$b = 4\, m/s^2$,and $c = 5\, m/s^3$. The force acting on the body at $t = 2\, s$ is ......... $N$.

$A$ body of mass $5 \ kg$ starts from the origin with an initial velocity $(30 \hat{i} + 40 \hat{j}) \ m/s$. If a constant force $-(\hat{i} + 5 \hat{j}) \ N$ acts on the body,then the time in which the $y$-component of its velocity becomes zero is (in $s$)

$A$ 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 ........... $m/s$.

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:

$A$ cricketer catches a ball of mass $150\; g$ in $0.1\; s$ moving with a speed of $20\; m/s$. The force experienced by the cricketer is ..... $N$.

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