<p>Two trains are traveling in the same direction on the same straight line, lev

Question

<p>Two trains are traveling in the same direction on the same straight line, level track. Train A in front is traveling at 10m/s and train B behind A is traveling at 60m/s<br />A) If the trains are initially 800m apart and do not change their speeds, in how many seconds will they collide?<br />B) when the trains are only 600m apart and still traveling at the same speeds, the two engineers see each other. Train A starts accelerating at a_A=+1m/s^{2 &#160;}and train B starts slowing down at a_B=1m/s². Will the two trains collide? If so how many seconds?^&#160;</p>

Explanation / Answer

relative velocity =60-10=50m/s
relative displacement s =800m
time after which they collide=s/v=800/50=16 sec


acceleration of train 1 a1=-1m/s^2
train 2 a2=1m/s^2
relative acceleration= -2m/s^2
relative distance s=600m
relative velocity=50m/s
s=ut+at^2/2
600=50t-t^2
t=20 sec

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