$A$ force of $50\, dynes$ acts on a body of mass $5\, g$ which is at rest for an interval of $3\, seconds$. The impulse is:

If impulse $I$ varies with time $t$ as $I \text{ (kg m s}^{-1}) = 20 t^2 - 40 t$. The change in momentum is minimum at ........... $s$.

In two different experiments,an object of mass $5 \; kg$ moving with a speed of $25 \; ms^{-1}$ hits two different walls and comes to rest within
$(i)$ $3 \; s$,$(ii)$ $5 \; s$,respectively.
Choose the correct option out of the following:

$A$ body of mass $m$ collides against a wall with a velocity $v$ and rebounds with the same speed. Its change of momentum is

$A$ $40 \ g$ ball dropped from a certain height bounces back from the horizontal ground without losing mechanical energy. If its speed is $10 \ m/s$ just before making contact with the ground,and the average value of the force of the ground on the ball is $16 \ N$ while the ball and ground are in contact,how long were they in contact in milliseconds $(ms)$?

$A$ particle of mass $m$,initially at rest,is acted on by a force $F = F_0 \left\{ {1 - {{\left( {\frac{{2t - T}}{T}} \right)}^2}} \right\}$ during the interval $0 \leq t \leq T$. The velocity of the particle at the end of the interval is: