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."