$A$ body of mass $M$ collides against a wall with a velocity $v$ and retraces its path with the same speed. The change in momentum is (take initial direction of velocity as positive).

$A$ force of $50 \, dynes$ acts on a particle of mass $5 \, g$ for $3 \, seconds$. What is the impulse of the force?

$A$ uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time (Take acceleration in the backward direction as positive).

Displacement of a particle of mass $2\, kg$ moving in a straight line varies with time as $s = (2t^3 + 2)\, m$. The impulse of the force acting on the particle over a time interval between $t = 0$ and $t = 1\, s$ is .......... $N-s$.

$A$ force-time graph for a linear motion is shown in the figure,where the segments are circular. The linear momentum gained between $0$ and $8$ seconds is

$A$ machine gun fires a bullet of mass $65 \, g$ with a velocity of $1300 \, m/s$. The man holding it can exert a maximum force of $169 \, N$ on the gun. The number of bullets he can fire per second will be ............