An object with a mass $10 \,kg$ moves at a constant velocity of $10 \,m/sec$. A constant force then acts for $4\, second$ on the object and gives it a speed of $2\, m/sec$ in opposite direction., the impulse acting on the object is ……… $newton \times \sec $

A particle of mass $m$, initially at rest, is acted upon by a variable force $F$ for a brief interval of time $T$. It begins to move with a velocity $u$ after the force stops acting. $F$ is shown in the graph as a function of time. The curve is a semicircle.

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m =0.4 kg$ is at rest on this surface. An impulse of $1.0 N s$ is applied to the block at time $t =0$ so that it starts moving along the $x$-axis with a velocity $v ( t )= v _0^{ e ^{-1 / \tau}}$, where $v_0$ is a constant and $\tau=4 s$. The displacement of the block, in metres, at $t=\tau$ is. . . . . . . Take $e ^{-1}=0.37$

A $100\, g$ iron ball having velocity $10 \,m/s$ collides with a wall at an angle $30^°$ and rebounds with the same angle. If the period of contact between the ball and wall is $0.1\, second$, then the force experienced by the wall is  ……….. $N$

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