$A$ particle moves in the $xy$-plane under the action of a force $\vec{F}$ such that the components of its linear momentum $\vec{p}$ at any time $t$ are $p_x = 2\cos t$ and $p_y = 2\sin t$. The angle between $\vec{F}$ and $\vec{p}$ at time $t$ is ........... $^o$.

$A$ time-varying force acts on a ball of mass $100 \ g$ for $2 \ ms$. The force versus time curve is shown below. If the initial speed of the ball is $10 \ m \ s^{-1}$,then the speed of the ball after $2 \ ms$ is: (in $m \ s^{-1}$)

$A$ 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

An engine pumps water continuously through a hose. Water leaves the hose with velocity $v$ and $m$ is the mass per unit length of the water jet. If this jet hits a surface and comes to rest instantaneously,the force on the surface is

$A$ soccer ball of mass $250 \text{ g}$ is moving horizontally to the left with a speed $22 \text{ ms}^{-1}$. This ball is kicked towards the right with a velocity $30 \text{ ms}^{-1}$ at an angle $53^{\circ}$ with the horizontal in the upward direction. Assuming that it took $0.01 \text{ s}$ for the collision to take place, the average force acting is $(\cos 53^{\circ} = \frac{3}{5}; \sin 53^{\circ} = \frac{4}{5})$. (in $\text{ N}$)

$A$ block of mass $2 \ kg$ is free to move along the $x$-axis. It is at rest and from $t=0$ onwards it is subjected to a time-dependent force $F(t)$ in the $x$ direction. The force $F(t)$ varies with $t$ as shown in the figure. The kinetic energy of the block after $4.5 \ s$ is (in $J$)