Question

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?

Answer 1

`"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."`