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:

$A$ constant retarding force of $50\; N$ is applied to a body of mass $20\; kg$ moving initially with a speed of $15\; m/s$. How long (in $sec$) does the body take to stop?

$A$ body of mass $1.5 \ kg$ is moving towards south with a uniform velocity of $8 \ ms^{-1}$. $A$ force of $6 \ N$ is applied to the body towards east. The displacement of the body $3 \ s$ after the application of the force is (in $m$)

$A$ body of mass $4 \ kg$ experiences two forces $\overrightarrow{F}_1 = 5 \hat{i} + 8 \hat{j} + 7 \hat{k}$ and $\overrightarrow{F}_2 = 3 \hat{i} - 4 \hat{j} - 3 \hat{k}$. The acceleration acting on the body is :

An object of mass $2 \, kg$ is placed at rest in a frame $S_1$ moving with velocity $10 \hat{i} + 5 \hat{j} \, m/s$ and having acceleration $5 \hat{i} + 10 \hat{j} \, m/s^2$. The object is also seen by an observer standing in a frame $S_2$ moving with velocity $5 \hat{i} + 10 \hat{j} \, m/s$. Calculate the net force acting on the object with respect to the $S_1$ frame.

$A$ constant force acting on a body of mass $5\,kg$ changes its speed from $5\,ms^{-1}$ to $10\,ms^{-1}$ in $10\,s$ without changing the direction of motion. The force acting on the body is ......... $N$.