The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from $0 \, s$ to $8 \, s$ is .......... $N-s$.

Consider the following statement: When jumping from some height,you should bend your knees as you come to rest,instead of keeping your legs stiff. Which of the following relations can be useful in explaining the statement?

$A$ ball of mass $150 \, g$ moving with a velocity of $12 \, m/s$ hits a bat and returns with a velocity of $20 \, m/s$ in the opposite direction within $0.01 \, s$. The force exerted by the bat on the ball is ........... $N$.

An average force of $125\,N$ is applied on a machine gun firing bullets each of mass $10\,g$ at the speed of $250\,m/s$ to keep it in position. The number of bullets fired per second by the machine gun is:

$A$ body of mass $5 \,kg$ is moving with a velocity of $\vec{v}=(2 \hat{i}+6 \hat{j}) \,m/s$ at $t=0 \,s$. After time $t=2 \,s$,the velocity of the body is $(10 \hat{i}+6 \hat{j}) \,m/s$. The change in momentum of the body is ......... $kg \cdot m/s$.

$A$ cricket ball of mass $250\, g$ collides with a bat with velocity $10\, m/s$ and returns with the same velocity within $0.01\, s$. The force exerted on the ball is ....... $N$.