$A$ particle moving with a uniform acceleration travels $24 \ m$ and $64 \ m$ in the first two consecutive intervals of $4 \ sec$ each. Its initial velocity is......$m/sec$.

The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time $t$ will be

The displacement of a particle moving in a straight line is given by the expression $x = A t^3 + B t^2 + C t + D$ in metres, where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is

$A$ truck moving with a constant velocity $12 \,m/s$ crosses a car moving from rest with uniform acceleration $2 \,m/s^2$. The distance the car has to travel from the starting point to cross the truck again is (in $\,m$)

$A$ car,starting from rest,accelerates at the rate $\alpha$ through a distance $d$,then continues at a constant speed for time $t$ and then decelerates at the rate of $\alpha/2$ to come to rest. If the total distance traveled is $15\, d$,then $d=$

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