$A$ rifle bullet loses $1/20^{th}$ of its velocity in passing through a wooden plank. The least number of planks required to stop the bullet is :-

The position of a particle moving along the $x$ axis is given by the equation $x = (10 + 6t - 3t^2) \ m$. The distance travelled by the particle from $t = 1 \ s$ to $t = 4 \ s$ is: (in $m$)

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3} \ m/s^2$ in the third second is:

The initial velocity of a body moving along a straight line is $7 \, m/s$. It has a uniform acceleration of $4 \, m/s^2$. The distance covered by the body in the $5^{th}$ second of its motion is .......... $m$.

$A$ train accelerates from rest at a constant rate $\alpha$ for distance $x_1$ and time $t_1$. After that,it retards to rest at a constant rate $\beta$ for distance $x_2$ and time $t_2$. Which of the following relations is correct?

The displacement of a particle after time $t$ is given by $x = (k/b^2)(1 - e^{-bt})$ where $b$ is a constant. What is the acceleration of the particle?