Question

Two trains R and S start from rest simultaneously from stations A and B facing
each other with accelerations 0.5 m/s2and 2/3 m/s2reaching their maximum speeds
of 90 kmph and 72 kmph respectively. If they cross each other midway between
the stations, find the distance between the stations and the time taken by each
other.

Answer 1

for train R:

a=0.5 m/s^2

v=90*5/18=25m/s

u=0 m/s

time taken to reach station B:

v=u+at

25=0+0.5t

t=25/0.5=50 s

S=ut+1/2at^2

S=1/2*0.5*50^2=625 m

For train S:

a=2/3 m/s^2

v=72*5/18=20 m/s

u=0 m/s

time taken to reach station A:

v=u+at

20=0+2/3t

t=30 s

S=ut+1/2at^2

S= 1/2*2/3*30^2=300 m

Distance between the stations = 625 -300=325 m

Time taken by train R = 50 sec

Time taken by train S =30 sec