Kinematics: Would you help me find the solution?

Two trains are on the same track and moving the same direction. Train 1 is behind train 2 and has velocity #30 ms^(-1)#. Second train has a velocity #9 ms^(-1)#. When the driver of first train saw a train in front of him, he push the brake system with acceleration #1.2 ms^(-2)#. The distance between these two trains is 180 meters. Do these two trains hit?

1 Answer
Feb 13, 2018

#"please look at the explanation section."#

Explanation:

#"the time required for train-1 to stop."#
#v=v_i-at#
#0=30-1.2t#

#t=30/1.2=25 sec#
#"the time required for train-1 to slow down to 9 " m / s:#

#9=30-1.2t#

#1.2t=30-9#

#1.2t=21#

#t=21/(1.2)=17.5 sec#

#"displacement of train-1 for 17.5 sec."#

#x_1=v_it-1/2 a t^2=30*17.5-1/2*1.2*(17.5)^2=341.25" "m#

#"displacement of train-2 for 17.5 sec."#

#x_2=180+9*17.5=337.5" "m#

#"train-1 hits to train-2 because "x_1>x_2."#