$A$ body of mass $10 \,kg$ is acted upon by a force given by the equation $F = (3t^2 - 30) \,N$. The initial velocity of the body is $10 \,m/s$. What is the velocity of the body after $5 \,s$ (in $\,m/s$)?

The force required to stop a body of mass $10 \,kg$ moving along a straight line path with a velocity of $10 \,ms^{-1}$ in a time of $10 \,s$ is (in $\,N$)

The variation of momentum $(p)$ with time $(t)$ for one of the bodies in a two-body collision is shown in the figure. The instantaneous force is maximum corresponding to which point?

$A$ body of mass $500\,g$ moves along the $x$-axis such that its velocity varies with displacement $x$ according to the relation $v = 10\sqrt{x}\,m/s$. The force acting on the body is $...........\,N$.

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

$A$ particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t = 0$,a force $F = kt$ acts in the same direction on the moving particle during time interval $T$ so that its momentum changes from $p$ to $3p$. Here $k$ is a constant. The value of $T$ is