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 body is moving from rest under constant acceleration and let ${S_1}$ be the displacement in the first $(p - 1)$ sec and ${S_2}$ be the displacement in the first $p\,\sec .$ The displacement in ${({p^2} - p + 1)^{th}}$ sec. 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 car is moving with speed of $150\,km / h$ and after applying the brake it will move $27\,m$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling $....m$ distance.

A motor car moving at a speed of $72\, km/h$ cannot come to a stop in less than $3.0\,\sec $ whilefor a truck this time interval is $5.0\,\sec $. On a highway, the car is behind the truck  both moving at $72\, km/h$. The truck gives a signal that it is going to stop at emergency. At what distance the car should be from the truck so that it does not bump onto (collide with) the truck. Human response time is $0.5\,\sec $.