$A$ 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 ratio of displacement in $n$ seconds and in the $n^{th}$ second for a particle moving in a straight line under constant acceleration starting from rest is:

$A$ driver applies the brakes on seeing the red traffic signal $400 \ m$ ahead. At the time of applying brakes,the vehicle was moving with $15 \ m/s$ and retarding at $0.3 \ m/s^2$. The distance of the vehicle from the traffic light one minute after the application of brakes is: (in $m$)

The same retarding force is applied to stop a train. The train stops after $80 \ m$. If the speed is doubled,then the stopping distance will be

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 ............ $\text{m/s}^2$.

$A$ body travels for $15\, s$ starting from rest with constant acceleration. If it travels distances ${S_1}$,${S_2}$,and ${S_3}$ in the first $5\, s$,the second $5\, s$,and the next $5\, s$ respectively,the relation between ${S_1}$,${S_2}$,and ${S_3}$ is: