An object at rest at the origin begins to move in the $+x$-direction with a uniform acceleration of $1 \,m / s ^2$ for $4 \,s$ and then it continues moving with a uniform velocity of $4 \,m / s$ in the same direction.The $x-t$ graph for object's motion will be

Two trains travelling on the same track are approaching each other with equal speeds of $40\, m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\, km$ apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be.........$m/{s^2}$

A particle moves for $8\, seconds$. It first accelerates from rest and then retards to rest. If the retardation be $3\, times$ the acceleration, then time for which it accelerates will be 

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

The velocity-time graphs of a car and a scooter are shown in the figure. $(i)$ the difference between the distance travelled by the car and the scooter in $15\, s$ and $(ii)$ the time at which the car will catch up with the scooter are, respectively