The position of a particle moving along the $x$-axis is given by $x = (-2t^3 + 3t^2 + 5) \ m$. The acceleration of the particle at the instant its velocity becomes zero is ....... $m/s^2$.

Two cars $A$ and $B$ are initially at rest at the same point. If car $A$ starts with a uniform velocity of $40\, m/s$ and car $B$ starts in the same direction with a constant acceleration of $4\, m/s^2$,then after how much time will car $B$ catch car $A$?

An object travelling at a speed of $36 \ km/h$ comes to rest in a distance of $200 \ m$ after the brakes are applied. The retardation produced by the brakes is (in $m/s^2$)

If a train travelling at $72 \text{ km/h}$ is to be brought to rest in a distance of $200 \text{ m}$,then its retardation should be ............ $\text{m/s}^2$.

$A$ particle is moving with constant acceleration $a$. The following graph shows the $v^{2}$ versus $x$ (displacement) plot. The acceleration of the particle is $...... \text{m/s}^{2}$.

The deceleration of a car traveling on a straight highway is a function of its instantaneous velocity $v$ given by $\omega = a \sqrt{v}$,where $a$ is a constant. If the initial velocity of the car is $v_0$,the distance the car will travel and the time it takes before it stops are: