$A$ cricket player catches a ball of mass $120 \,g$ moving with $25 \,m/s$ speed. If the catching process is completed in $0.1 \,s$, then the magnitude of force exerted by the ball on the hand of the player will be (in $SI$ unit):

$A$ 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 maximum acceleration of a $5\,kg$ block is $.............\,m/s^{2}$.

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

The momentum $p$ (in $kg \cdot m/s$) of a particle is varying with time $t$ (in $s$) as $p = 2 + 3t^2$. The force acting on the particle at $t = 3 \, s$ will be ......... $N$.

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