particles A and B are moving along horizontal straight lines which lie in the west east direction. At a certain time, A passes a point P moving to the east with speed 5ms^-1 and constant acceleration 1ms^-2. Simultaneously, B passes a point Q east of P with speed 4ms^-1 towards the west but with constant acceleration 2ms^-2 towards the east. Given that the distance PQ is 28m, Calculate
a) The distance of A from P when B reverse direction
b) The time taken after the start for A to overtake
c) The further time taken for B to overtake A

Question

particles A and B are moving along horizontal straight lines which lie in the west east direction. At a certain time, A passes a point P moving to the east with speed 5ms^-1 and constant acceleration 1ms^-2. Simultaneously, B passes a point Q east of P with speed 4ms^-1 towards the west but with constant acceleration 2ms^-2 towards the east. Given that the distance PQ is 28m, Calculate 
a) The distance of A from P when B reverse direction 
b) The time taken after the start for A to overtake 
c) The further time taken for B to overtake A

farcher · Answer

There are many ways of solving such problems.
One way is to sketch velocity time graphs and find the area under a graph which is the displacement of the particle.
All the parts cab be done this way or by using the appropriate linematic equations for constant acceleration.
However I feel that parts b and c are easiest done using relative velocity and relative acceleration as shown on the attachment.