$A$ particle moving along the $X$-axis has acceleration $f$ at time $t$ given by $f=f_0\left(1-\frac{t}{T}\right)$,where $f_0$ and $T$ are constants. The particle at $t=0$ has zero velocity. In the time interval between $t=0$ and the instant when $f=0$,the particle's velocity is

$A$ particle is moving along the $X$-axis with velocity $v = e^{-\beta x}$. At time $t = 0$,the particle is located at $x = 0$. The displacement of the particle as a function of time is

$A$ body travels in a straight line from point $A$ to point $B$ with an initial velocity zero and uniform acceleration, covering $1 \,m$ during the first second and $39 \,m$ during the last second. The distance between $A$ and $B$ in metre is

$A$ bullet loses $1/20$ of its velocity after passing through a wooden plank. What is the minimum number of such planks required to stop the bullet completely?

$A$ small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of $10 \, m$ in $t \, s$,the distance travelled by the toy in the next $t \, s$ will be ......... $m$.

$A$ three-wheeler starts from rest,accelerates uniformly with $1\; m/s^{2}$ on a straight road for $10\; s$,and then moves with uniform velocity. Plot the distance covered by the vehicle during the $n^{\text{th}}$ second $(n = 1, 2, 3, \ldots)$ versus $n$. What do you expect this plot to be during accelerated motion: a straight line or a parabola?