The driver of a bus moving with a velocity of $72 \ km/h$ observes a boy walking across the road at a distance of $50 \ m$ in front of the bus and decelerates the bus at $5 \ m/s^2$ by applying brakes and is just able to avoid an accident. The reaction time of the driver is (in $s$)

The engine of a motorcycle can produce a maximum acceleration $5 \, m/s^2$. Its brakes can produce a maximum retardation $10 \, m/s^2$. What is the minimum time in which it can cover a distance of $1.5 \, km$?

Two trains '$A$' and '$B$' of length '$l$' and '$4l$' are travelling into a tunnel of length '$L$' on parallel tracks from opposite directions with velocities $108\,km/h$ and $72\,km/h$,respectively. If train '$A$' takes $35\,s$ less time than train '$B$' to cross the tunnel,then the length '$L$' of the tunnel is $...........\,m$. (Given $L = 60l$)

$A$ particle has an initial velocity of $10 \, m/s$. It moves due to a constant retarding force along the line of motion,which produces a retardation of $5 \, m/s^2$. Then:

At time $t=0$,a particle leaves the origin and moves in the positive direction of the $X$-axis. If the velocity of the particle varies as $v(t)=v_0(1-t/t_0)$,where $|v_0|=10 \ m/s$ and $t_0=10 \ s$,then the distance covered by the particle during the first $20 \ s$ is: (in $m$)

Look at the graphs $(a)$ to $(d)$ carefully and state,with reasons,which of these cannot possibly represent one-dimensional motion of a particle.