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

A gun applies a force $F$ on a bullet which is given by $F =\left(100-0.5 \times 10^{5} t \right) N$. The bullet emerges out with speed $400 \,m / s$. Then find out the impulse exerted till force on bullet becomes zero. (in $N - s$)

A body of mass $M$ hits normally a rigid wall with velocity $V$ and bounces back with the same velocity. The impulse experienced by the body is

The figure shows the position - time $(x-t)$ graph of one-dimensional motion of the body of mass $0.4\; kg$. The magnitude of each impulse is 

The linear momentum $p$ of a body of mass $5 \,kg$ varies with time $t$ as, $p = 5t^2 + t + 5$ It follows that the body is moving with

A body is accelerated by applying a force of $30\,N$. The change in the momentum of the body after $2\,sec$ is ............ $kg-m/s$