The motion of a particle along a straight line is described by the equation $x = 8 + 12t - t^3$,where $x$ is in meters and $t$ is in seconds. The retardation of the particle when its velocity becomes zero is .......... $m/s^2$.

$A$ car moving at a speed of $50 \, km/hr$ stops after covering a distance of $6 \, m$ upon applying brakes. If the same car is moving at a speed of $100 \, km/hr$,what distance (in $m$) will it cover after applying the brakes?

$A$ student is at a distance of $16 \ m$ from a bus when the bus begins to move with a constant acceleration of $9 \ m \ s^{-2}$. The minimum velocity with which the student should run towards the bus so as to catch it is $\alpha \sqrt{2} \ m \ s^{-1}$. The value of $\alpha$ is

Stopping distance of vehicles: When brakes are applied to a moving vehicle,the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity $(v_0)$ and the braking capacity,or deceleration,$-a$ that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of $v_0$ and $a$.

$A$ body is moving along a straight line with initial velocity $v_0$. Its acceleration $a$ is constant. After $t$ seconds,its velocity becomes $v$. The average velocity of the body over the given time interval is

The speeds of two identical cars are $u$ and $4u$ at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is